- A square garden has a side length of 15 feet. A brick path that is 3 feet wide is built around the entire outside of the garden. What is the perimeter of the outer edge of the brick path?
Answer: 84 feet
The garden is a 15-foot square. The 3-foot path adds 3 feet to the top, bottom, left, and right. The new, larger square (garden plus path) has a side length of 15 + 3 + 3 = 21 feet. The perimeter of this new square is 4 × 21 = 84 feet.
- A rectangular flower bed that is 12 meters long and 5 meters wide is built against a long brick wall. Fencing is put around the other three sides of the flower bed. What is the total length of the fencing used?
Answer: 22 meters
The fencing is needed for two sides of 5 meters and one side of 12 meters. The side against the wall does not need fencing. The total length of fencing is 5 meters + 12 meters + 5 meters = 22 meters.
- A large rectangular piece of paper is 10 inches by 8 inches. A small square with a side length of 3 inches is cut out from one of the corners. What is the perimeter of the new shape?
Answer: 36 inches
The perimeter of the original rectangle is 2 × (10 + 8) = 36 inches. When a square is cut from a corner, two sides of the rectangle are shortened by 3 inches each, but two new sides of 3 inches each are created. The change in perimeter is -3 -3 + 3 + 3 = 0. Therefore, the perimeter of the new shape is the same as the original rectangle, 36 inches.
- A rectangular photograph is 7 inches wide and 9 inches tall. It is placed in a frame that adds a border of 2 inches to every side. What is the perimeter of the outside edge of the framed photograph?
Answer: 48 inches
The frame adds 2 inches to each side. The new width is 7 + 2 + 2 = 11 inches. The new height is 9 + 2 + 2 = 13 inches. The perimeter of the outside of the frame is P = 2 × (11 + 13) = 2 × 24 = 48 inches.
- An L-shaped room has six walls. The outside wall measurements are 12 feet, 15 feet, 7 feet, 6 feet, 5 feet, and 9 feet. What is the perimeter of the room?
Answer: 54 feet
The perimeter of a shape is the sum of the lengths of all its sides. To find the perimeter of the L-shaped room, add all the given wall measurements: 12 + 15 + 7 + 6 + 5 + 9 = 54 feet.
- A shape is made by joining three identical squares in a row, side to side. If the side of each square is 4 centimeters, what is the perimeter of the entire shape?
Answer: 32 cm
The shape is a long rectangle composed of three squares. The top side has a length of 4+4+4=12 cm. The bottom side also has a length of 12 cm. The left and right sides each have a length of 4 cm. The perimeter is the sum of the outside edges: 12 + 12 + 4 + 4 = 32 cm. Alternatively, there are 8 exterior sides of length 4 cm, so 8 x 4 = 32 cm.
- A triangle has a perimeter of 30 feet. The second side is 2 feet longer than the first side. The third side is 4 feet longer than the first side. What is the length of the shortest side?
Answer: 8 feet
Let the shortest side be 'x'. The other sides are 'x + 2' and 'x + 4'. The perimeter is the sum of the sides: x + (x + 2) + (x + 4) = 30. This simplifies to 3x + 6 = 30. Subtract 6 from both sides: 3x = 24. Divide by 3: x = 8. The shortest side is 8 feet.
- A rectangle has a perimeter of 50 feet. Its length is 15 feet. What is its width?
Answer: 10 feet
The perimeter of a rectangle is P = 2 × length + 2 × width. We know P=50 and length=15. So, 50 = 2 × 15 + 2 × width. This simplifies to 50 = 30 + 2 × width. Subtract 30 from both sides: 20 = 2 × width. Divide by 2 to find the width: width = 10 feet.
- The perimeter of an equilateral triangle is 27 centimeters. What is the length of one of its sides?
Answer: 9 centimeters
An equilateral triangle has three sides of equal length. To find the length of one side, divide the total perimeter by 3. Side length = 27 cm / 3 = 9 cm.
- A large rectangle is 20 feet long and 10 feet wide. A smaller rectangular porch that is 6 feet long and 4 feet wide juts out from the middle of one of the 20-foot sides. What is the perimeter of the combined shape of the house and porch?
Answer: 68 feet
Start with the perimeter of the large rectangle: 2 * (20 + 10) = 60 feet. When the porch is added, a 6-foot section of the house's wall is replaced by the three outer walls of the porch. The lengths of these three walls are 4 feet, 6 feet, and 4 feet. The change to the perimeter is -6 (the removed wall section) + 4 + 6 + 4 = +8 feet. The new total perimeter is 60 + 8 = 68 feet.
- A rectangular poster has a width of 10 inches. Its length is 4 inches greater than its width. What is the perimeter of the poster?
Answer: 48 inches
First, determine the length of the poster. The width is 10 inches, and the length is 4 inches greater, so the length is 10 + 4 = 14 inches. The perimeter of a rectangle is P = 2 × (length + width). So, P = 2 × (14 + 10) = 2 × 24 = 48 inches.
- A triangular garden has sides measuring 2 feet, 30 inches, and 3 feet. What is the perimeter of the garden in inches? (1 foot = 12 inches)
Answer: 90 inches
To find the perimeter in inches, first convert all measurements to inches. The first side is 2 feet × 12 inches/foot = 24 inches. The second side is 30 inches. The third side is 3 feet × 12 inches/foot = 36 inches. Now, add the lengths of the three sides: 24 + 30 + 36 = 90 inches.
- Two identical squares, each with a side length of 5 cm, are placed side-by-side to form a single, larger rectangle. What is the perimeter of this new rectangle?
Answer: 30 cm
When two 5 cm squares are placed side-by-side, they form a rectangle with a length of 5 + 5 = 10 cm and a width of 5 cm. The perimeter of this new rectangle is P = 2 × (10 + 5) = 2 × 15 = 30 cm.
- A square has a side length of 8 cm. A rectangle has a length of 10 cm and a width of 5 cm. What is the difference between the perimeter of the square and the perimeter of the rectangle?
Answer: 2 cm
First, find the perimeter of the square: P_square = 4 × 8 cm = 32 cm. Next, find the perimeter of the rectangle: P_rectangle = 2 × (10 cm + 5 cm) = 2 × 15 cm = 30 cm. The difference is 32 cm - 30 cm = 2 cm.
- A rectangular backyard is 25 feet long and 18 feet wide. The entire yard is enclosed by a fence, but there is a 3-foot wide gate in the fence. How many feet of fencing material were used, not including the gate?
Answer: 83 feet
First, calculate the total perimeter of the backyard: P = 2 × (25 + 18) = 2 × 43 = 86 feet. The gate is part of this perimeter, but it is not made of fencing material. So, subtract the width of the gate from the total perimeter: 86 feet - 3 feet = 83 feet. Therefore, 83 feet of fencing material were used.
- The perimeter of a square painting is 48 inches. What is the length of one side of the painting?
Answer: 12 inches
A square has four equal sides. The perimeter is the sum of the lengths of all four sides, so P = 4 × side. To find the length of one side, divide the perimeter by 4. Side = 48 inches / 4 = 12 inches.
- An isosceles triangle has a perimeter of 40 inches. The shortest side, which is the base, measures 10 inches. What is the length of one of the two equal sides?
Answer: 15 inches
The perimeter is the sum of the three sides. Let the length of one of the equal sides be 's'. The perimeter is s + s + 10 = 40 inches. Combining the 's' terms gives 2s + 10 = 40. Subtract 10 from both sides: 2s = 30. Divide by 2 to find s: s = 15 inches.
- A figure in the shape of a plus sign is made from five identical squares, each with a side length of 3 inches. What is the perimeter of the plus-sign shape?
Answer: 36 inches
The plus-sign shape has 12 sides on its exterior. Each of these sides is a side of one of the squares, so each has a length of 3 inches. The total perimeter is the number of exterior sides multiplied by the length of a side: 12 × 3 inches = 36 inches.
- A rectangular field has a length of 30 meters and a width of 20 meters. A farmer walks around the entire edge of the field one time. What is the total distance the farmer walks?
Answer: 100 meters
The distance around the edge of a field is its perimeter. The formula for the perimeter of a rectangle is P = 2 × (length + width). In this case, P = 2 × (30 meters + 20 meters) = 2 × (50 meters) = 100 meters. The farmer walks 100 meters.
- A regular hexagon has six equal sides. If one side of a regular hexagon measures 8 meters, what is its perimeter?
Answer: 48 meters
A regular hexagon has 6 equal sides. The perimeter is the total length around the shape. To find the perimeter, multiply the length of one side by the number of sides: 8 meters/side × 6 sides = 48 meters.
