Isosceles Triangles
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Math › Isosceles Triangles
An isoceles triangle has a base angle that is twice the vertex angle. What is the sum of the base and vertex angles?
Explanation
All triangles have 
Let 
So the equation to solve becomes:
Thus 
The sum of the vertex and one base angle is 
One side of a regular hexagon is 20% shorter than one side of a regular pentagon. Which is the greater quantity?
(A) The perimeter of the pentagon
(B) The perimeter of the hexagon
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
Explanation
Let 
Each side of the hexagon is 20% less than this length, or
The perimeter is five times this, or 
Since 
What is the length of a rectangular room with a perimeter of 
Explanation
We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.
Subtract 
Divide 
Angela has a garden that she wants to put a fence around. How much fencing will she need if her garden is 
Explanation
The fence is going around the garden, so this is a perimeter problem.
The sum of the lengths of three sides of a regular pentagon is one foot. Give the perimeter of the pentagon in inches.
It is impossible to determine the perimeter from the information given.
Explanation
A regular pentagon has five sides of the same length.
One foot is equal to twelve inches; since the sum of the lengths of three of the congruent sides is twelve inches, each side measures
The perimeter is
What is the perimeter of a square with area 196 square inches?
It cannot be determined from the information given.
Explanation
A square with area 196 square inches has sidelength 
One side of a regular pentagon is 20% longer than one side of a regular hexagon. Which is the greater quantity?
(A) The perimeter of the pentagon
(B) The perimeter of the hexagon
(A) and (B) are equal
(B) is greater
(A) is greater
It is impossible to determine which is greater from the information given
Explanation
Let 
Each side of the pentagon is 20% greater than this length, or
The perimeter is five times this, or 
The perimeters are the same.
A rectangle is two feet longer than it is wide; its perimeter is 11 feet. What is its area in square inches?
It is impossible to determine the area from the information given
Explanation
The length of the rectangle is 2 feet, or 24 inches, greater than the width, so, if 
The perimeter of the rectangle is 11 feet, or 
The width is 21 inches, and the length is 45 inches. The area is their product:
Which is the greater quantity?
(a) The perimeter of
(b) The perimeter of
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) is greater.
(b) is greater.
Explanation
No information is given about the legs of either triangle; therefore, no information about their perimeters can be deduced.
Which quantity is greater?
(a) The perimeter of a square with area 10,000 square centimeters
(b) The perimeter of a rectangle with area 8,000 square centimeters
It is impossible to tell from the information given
(a) and (b) are equal
(b) is greater
(a) is greater
Explanation
A square with area 10,000 square centimeters has sidelength 
Not enough information is given about the rectangle with area 8,000 square centimeters to determine its perimeter. For example, if its dimensions are 100 centimeters by 80 centimeters, its perimeter is 
