To review these concepts, go to Perimeter Word Problems Study Guide.

**Perimeter Word Problems Practice Questions**

**Practice
**

**Problems**

- The measure of the base of an isosceles triangle is 10 units. If the legs each measure 2 units more than the base, what is the perimeter of the triangle?
- The sides of a scalene triangle are 12, 15, and 20 units, respectively. What is the perimeter of the triangle?
- A side of a square is represented by the expression 5
*x*. If the perimeter is 40 units, what is the length of one side of the square? - The length of a rectangle is three times its width. If the perimeter of the rectangle is 80 meters, what is the length of the rectangle?
- An area is enclosed with a fence in the shape of a regular pentagon. If each side of fencing is 35 meters long, what is the perimeter of the pentagon?
- A regular octagon has sides that each measure 20 cm. What is the perimeter of the octagon?

**Solutions**

*Read and understand the question*. This question is looking for the perimeter of an isosceles triangle.*Read and understand the question*. This question is looking for the perimeter of a scalene triangle.*Read and understand the question*. This question is looking for the side of a square when an expression for the sides and the perimeter is known.*Make a plan*. The perimeter is the distance around the object. Since the figure is a square, each of the sides are of equal length. Use 5*x*for the length of each of the four sides.*Carry out the plan*. Add the expression that represents each side, and set the value equal to 40. Then solve for*x*.- 5

*x*+ 5*x*+ 5*x*+ 5*x*= 40Combine like terms.

- 20

*x*= 40Divide each side by 20 to get

*x*= 2. Substitute*x*= 2 into 5*x*to get the length of one side.- 5(2) = 10

The length of one side is 10 units. Another way to solve this question is to use that fact that the figure is a square and the perimeter is 40. Divide 40 by 4 to get a side length of 10 units.

*Check your answer*. To check this solution, add the four sides to be sure the perimeter is 40.- 10 + 10 + 10 + 10 = 40

so this solution is checking.

*Read and understand the question*. This question is looking for the length of the rectangle when the relationship between the length and the width is given, along with the perimeter.*Read and understand the question*. This question is looking for the perimeter of a regular pentagon.*Read and understand the question*. This question is looking for the perimeter of a regular octagon.

*Make a plan*. The perimeter is the distance around the object. Add the lengths of the three sides of the triangle to find the perimeter. The length of the base is given.

*Carry out the plan*. The lengths of the two legs of the triangle are two more than the length of the base side: 10 + 2 = 12. Add the three sides: 10 + 12 + 12 = 34 meters. The perimeter is 34 meters.

*Check your answer*. To check this solution, start with the perimeter of 34 meters. If each side length is subtracted from this value, the result should be zero: 34 – 10 – 12 – 12 = 0, so this solution is checking.

*Make a plan*. The perimeter is the distance around the object. Add the lengths of the three sides of the triangle to find the perimeter. All three side lengths are given.

*Carry out the plan*. Add the three side lengths: 12 + 15 + 20 = 47 meters.

The perimeter is 47 meters.

*Check your answer*. To check this solution, start with the perimeter of 47 meters. If each side length is subtracted from this value, the result should be zero: 47 – 12 – 15 – 20 = 0, so this solution is checking.

*Make a plan*. Use the relationship between the length and width to write let statements. Then, add the four sides together and set the equation equal to 80.

*Carry out the plan*. The length is three times the width, so let w = width, and let 3w = length. The perimeter is w + 3w + w + 3w = 80. Simplify to get 8w = 80. Divide each side by 8 to get w = 10. The length is 3(10) = 30 meters.

*Check your answer*. To check your solution, substitute w = 10 into the perimeter formula to make sure that the perimeter is equal to 80 meters.

Since w = 10, 3w = 3(10) = 30. Adding the four sides becomes 10 + 30 + 10 + 30 = 80. This answer is checking.

*Make a plan*. The perimeter is the distance around an object. A regular pentagon is a five-sided polygon where each side has the same measure. Each side of the fence is 35 meters long.

*Carry out the plan*. Add the sides: 35 + 35 + 35 + 35 + 35, or 5 × 35 = 175.

The perimeter is 175 meters.

*Check your answer*. To check this solution, start with the perimeter of 175 meters. If each side length is subtracted from this value, the result should be zero.

- 175 – 35 – 35 – 35 – 35 – 35 = 0

so this solution is checking.

*Make a plan*. The perimeter is the distance around an object. A regular octagon is an eight-sided polygon where each side has the same measure.

Each side is 20 cm.

*Carry out the plan*. Add the sides: 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20, or 8 × 20 = 160. The perimeter is 160 cm.

*Check your answer*. To check this solution, start with the perimeter of 160 units. If each side length is subtracted from this value, the result should be zero.

- 160 – 20 – 20 – 20 – 20 – 20 – 20 – 20 – 20 = 0

so this solution is checking.

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