Find the perimeter of the triangular sandbox

A park has a triangular sandbox. Todd wants to create a smaller sandbox at his backyard having the same angles as the park sandbox.
Drawings of both sandboxes are shown.

What is the perimeter, in feet (ft), of Todd’s sandbox?

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Use proportions to find the two missing sides of Todd’s sandbox.​

For the left side of the sandbox:

​{created a proportion comparing the sides of the large triangle to the sides of the small triangle}

20x = 112
​x = 5.6

The left side of Todd’s sandbox is 5.6 ft.


For the right side of the sandbox:

​{created a proportion comparing the sides of the large triangle to the sides of the small triangle}

20x = 144 {cross-multiplied}
​x = 7.2 {divided}

The right side of Todd’s sandbox is 7.2 ft.

To find the perimeter of Todd’s sandbox, add up the sides of the triangle:
8 + 5.6 + 7.2
= 20.8

The perimeter of Todd’s sandbox is 20.8 ft.

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