Question

Round your answer to tenth place. 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. 14 ft 18 ft 20 ft Park Sandbox 8 ft Todd's Sandbox What is the perimeter, in feet (ft), of Todd's sandbox? DOLL​

Answer 1

To find the perimeter of Todd's sandbox, you can use similar triangles and proportions to find the lengths of the sides. The perimeter of Todd's sandbox is 33.43 ft.

Step-by-step explanation:

To find the perimeter of Todd's sandbox, we need to add up the lengths of all three sides. From the diagram, we can see that one side of Todd's sandbox is 8 ft. Since the sandbox has the same angles as the park sandbox, we can use the proportional sides to find the lengths of the other two sides. The ratio of corresponding sides in similar triangles is equal. So, we can set up the proportion:

(8 ft / 14 ft) = (x / 20 ft)

Cross-multiplying, we get:

14x = 8 * 20

x = (8 * 20) / 14

x = 11.43 ft (rounded to tenth place)

Now we can find the perimeter:

Perimeter = 8 ft + 14 ft + 11.43 ft = 33.43 ft (rounded to tenth place)