If figure B is similar to figure A by a scale factor, then the perimeter of B is equal to the perimeter of A times the scale factor.
1920 inches or 160 feet
Practice makes perfect
In the plan of a skate park, we are given the following rectangle.
The actual length of WX is 50 feet. We also know that the perimeter of the rectangle — which is the perimeter of the skate park in the plan — is 80 inches. We want to find the perimeter of the actual skate park. Let's start by writing the actual length of WX in inches using the fact that 1 feet is equal to 12 inches. To do so, we need to multiply this length by 12.
50(12)=600Therefore, the actual length of WX is 600 inches. Next, we will recall the relationship between the perimeters of similar figures.
Perimeter of Similar Figures
If figure B is similar to figure A by a scale factor, then the perimeter of B is equal to the perimeter of A times the scale factor.
We can find the scale factor between the plan and the actual skate park. To do so, we will calculate the quotient of the two corresponding side lengths.
Length ofWXin the plan/Actual length of WX substitute ⟶ 600in./25in. = 24
We got that the scale factor is 24. Finally, we will find the perimeter of the actual skate park by multiplying the perimeter of the rectangle in the plan by 24.
80( 24) = 1920
The perimeter of the actual skate park is 1920 inches. To get the perimeter in feet, we need to divide the perimeter expressed in inches by 12.
1920/12=160
Therefore, the perimeter of the actual skate park is 1920 inches or 160 feet.
