Calculating the length of a side of a polygon - GMAT Quantitative
Card 1 of 72
A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
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If each of the five congruent sides has measure 
, then the other two sides have measures 
and 
. Add the sides to get the perimeter, which is equal to 5,280 feet, the solve for 
:
Each of the shortest sides is 996 feet long; the longest side is 
feet long.
If each of the five congruent sides has measure
Each of the shortest sides is 996 feet long; the longest side is
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The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
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One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or 
feet.
Multiply by 12 to convert to inches: 
inches.
One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or
Multiply by 12 to convert to inches:
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The perimeter of a regular pentagon is one-fifth of a mile. Give its sidelength in feet.
The perimeter of a regular pentagon is one-fifth of a mile. Give its sidelength in feet.
Tap to reveal answer
One mile is 5,280 feet. The perimeter of the pentagon is one-fifth of this, or 
feet. Since each side of a regular pentagon is congruent, the length of one side is one fifth-of this, or 
feet.
One mile is 5,280 feet. The perimeter of the pentagon is one-fifth of this, or
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The perimeter of a regular octagon is two kilometers. Give its sidelength in meters.
The perimeter of a regular octagon is two kilometers. Give its sidelength in meters.
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One kilometer is equal to 1,000 meters, so two kilometers comprise 2,000 meters. A regular octagon has eight sides of equal length, so divide by 8 to get the sidelength: 
meters.
One kilometer is equal to 1,000 meters, so two kilometers comprise 2,000 meters. A regular octagon has eight sides of equal length, so divide by 8 to get the sidelength:
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The perimeter of a regular pentagon is three kilometers. Give its sidelength in meters.
The perimeter of a regular pentagon is three kilometers. Give its sidelength in meters.
Tap to reveal answer
One kilometer is equal to 1,000 meters, so two kilometers comprise 3,000 meters. A regular pentagon has five sides of equal length, so divide by 5 to get the sidelength: 
meters.
One kilometer is equal to 1,000 meters, so two kilometers comprise 3,000 meters. A regular pentagon has five sides of equal length, so divide by 5 to get the sidelength:
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Six regular polygons each have perimeter one mile. The polygons are an equilateral triangle, a square, a pentagon, a hexagon, an octagon, and a decagon (ten-sided polygon). What is the mean of their sidelengths?
Six regular polygons each have perimeter one mile. The polygons are an equilateral triangle, a square, a pentagon, a hexagon, an octagon, and a decagon (ten-sided polygon). What is the mean of their sidelengths?
Tap to reveal answer
The sidelength of a regular polygon is the perimeter of one mile, or 5,280 feet, divided by the number of sides. Therefore, the sidelengths of the six shapes are:
Triangle: 
Square: 
Pentagon: 
Hexagon: 
Octagon: 
Decagon: 
The mean of the six sidelengths:
feet
The sidelength of a regular polygon is the perimeter of one mile, or 5,280 feet, divided by the number of sides. Therefore, the sidelengths of the six shapes are:
Triangle:
Square:
Pentagon:
Hexagon:
Octagon:
Decagon:
The mean of the six sidelengths:
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If the shape 
is a regular hexagon with side length of 
and a perimeter of 
meters, what is the length of one side?
If the shape
Tap to reveal answer
Perimeter is the total distance around a shape. Here we have a regular (all sides are equal) hexagon with side distance 2x+6. Multiplying this expression by 6 gives us our perimeter.
But we are not done yet. We need to plug this back in to get the side length
so 15 meters
Alternatively, we could divide 72 by 6 to get 12 meters.
Perimeter is the total distance around a shape. Here we have a regular (all sides are equal) hexagon with side distance 2x+6. Multiplying this expression by 6 gives us our perimeter.
But we are not done yet. We need to plug this back in to get the side length
so 15 meters
Alternatively, we could divide 72 by 6 to get 12 meters.
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A regular hexagon has perimeter 
. Which of the following is equal to the length of one side?
A regular hexagon has perimeter
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A hexagon has six sides of equal length, so divide the perimeter by 6, which is the product of 2 and 3:
A hexagon has six sides of equal length, so divide the perimeter by 6, which is the product of 2 and 3:
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A regular octagon has perimeter 
. Give the length of one of its sides.
A regular octagon has perimeter
Tap to reveal answer
A regular octagon has eight sides of equal length, so divide the perimeter by 8, or equivalently, 
:
.
A regular octagon has eight sides of equal length, so divide the perimeter by 8, or equivalently,
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A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
Tap to reveal answer
If each of the five congruent sides has measure , then the other two sides have measures and . Add the sides to get the perimeter, which is equal to 5,280 feet, the solve for :
Each of the shortest sides is 996 feet long; the longest side is feet long.
If each of the five congruent sides has measure
Each of the shortest sides is 996 feet long; the longest side is
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The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
Tap to reveal answer
One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or feet.
Multiply by 12 to convert to inches: inches.
One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or
Multiply by 12 to convert to inches:
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The perimeter of a regular pentagon is one-fifth of a mile. Give its sidelength in feet.
The perimeter of a regular pentagon is one-fifth of a mile. Give its sidelength in feet.
Tap to reveal answer
One mile is 5,280 feet. The perimeter of the pentagon is one-fifth of this, or feet. Since each side of a regular pentagon is congruent, the length of one side is one fifth-of this, or feet.
One mile is 5,280 feet. The perimeter of the pentagon is one-fifth of this, or
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The perimeter of a regular octagon is two kilometers. Give its sidelength in meters.
The perimeter of a regular octagon is two kilometers. Give its sidelength in meters.
Tap to reveal answer
One kilometer is equal to 1,000 meters, so two kilometers comprise 2,000 meters. A regular octagon has eight sides of equal length, so divide by 8 to get the sidelength: meters.
One kilometer is equal to 1,000 meters, so two kilometers comprise 2,000 meters. A regular octagon has eight sides of equal length, so divide by 8 to get the sidelength:
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The perimeter of a regular pentagon is three kilometers. Give its sidelength in meters.
The perimeter of a regular pentagon is three kilometers. Give its sidelength in meters.
Tap to reveal answer
One kilometer is equal to 1,000 meters, so two kilometers comprise 3,000 meters. A regular pentagon has five sides of equal length, so divide by 5 to get the sidelength: meters.
One kilometer is equal to 1,000 meters, so two kilometers comprise 3,000 meters. A regular pentagon has five sides of equal length, so divide by 5 to get the sidelength:
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Six regular polygons each have perimeter one mile. The polygons are an equilateral triangle, a square, a pentagon, a hexagon, an octagon, and a decagon (ten-sided polygon). What is the mean of their sidelengths?
Six regular polygons each have perimeter one mile. The polygons are an equilateral triangle, a square, a pentagon, a hexagon, an octagon, and a decagon (ten-sided polygon). What is the mean of their sidelengths?
Tap to reveal answer
The sidelength of a regular polygon is the perimeter of one mile, or 5,280 feet, divided by the number of sides. Therefore, the sidelengths of the six shapes are:
Triangle:
Square:
Pentagon:
Hexagon:
Octagon:
Decagon:
The mean of the six sidelengths:
feet
The sidelength of a regular polygon is the perimeter of one mile, or 5,280 feet, divided by the number of sides. Therefore, the sidelengths of the six shapes are:
Triangle:
Square:
Pentagon:
Hexagon:
Octagon:
Decagon:
The mean of the six sidelengths:
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If the shape is a regular hexagon with side length of and a perimeter of meters, what is the length of one side?
If the shape
Tap to reveal answer
Perimeter is the total distance around a shape. Here we have a regular (all sides are equal) hexagon with side distance 2x+6. Multiplying this expression by 6 gives us our perimeter.
But we are not done yet. We need to plug this back in to get the side length
so 15 meters
Alternatively, we could divide 72 by 6 to get 12 meters.
Perimeter is the total distance around a shape. Here we have a regular (all sides are equal) hexagon with side distance 2x+6. Multiplying this expression by 6 gives us our perimeter.
But we are not done yet. We need to plug this back in to get the side length
so 15 meters
Alternatively, we could divide 72 by 6 to get 12 meters.
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A regular hexagon has perimeter . Which of the following is equal to the length of one side?
A regular hexagon has perimeter
Tap to reveal answer
A hexagon has six sides of equal length, so divide the perimeter by 6, which is the product of 2 and 3:
A hexagon has six sides of equal length, so divide the perimeter by 6, which is the product of 2 and 3:
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A regular octagon has perimeter . Give the length of one of its sides.
A regular octagon has perimeter
Tap to reveal answer
A regular octagon has eight sides of equal length, so divide the perimeter by 8, or equivalently, :
.
A regular octagon has eight sides of equal length, so divide the perimeter by 8, or equivalently,
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A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
A pentagon with a perimeter of one mile has three congruent sides; one of the other sides is 100 feet longer than any of those three congruent sides, and the remaining side is 100 feet longer than that fourth side. What is the length of that longest side?
Tap to reveal answer
If each of the five congruent sides has measure , then the other two sides have measures and . Add the sides to get the perimeter, which is equal to 5,280 feet, the solve for :
Each of the shortest sides is 996 feet long; the longest side is feet long.
If each of the five congruent sides has measure
Each of the shortest sides is 996 feet long; the longest side is
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The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
The perimeter of a regular hexagon is one-half of a mile. Give the sidelength in inches.
Tap to reveal answer
One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or feet.
Multiply by 12 to convert to inches: inches.
One mile is 5,280 feet. The perimeter of the hexagon is one-half of this, or 2,640 feet. Since each side of a regular hexagon is congruent, the length of one side is one-sixth of this, or
Multiply by 12 to convert to inches:
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