Question

A playground is rectangular in shape. The longer side of the playground is 400 feet. A walkway runs diagonally through the playground. The angle formed by the walkway and the shorter side of the playground is 53°.
What is the perimeter of the playground?



Enter your answer, rounded to the nearest foot.

Answer 1

To find the perimeter, you need to find the width first. The angle of the diagonal line would reflect the ratio of the length:width. The equation would be:

length/width= tan 53
400ft/width= 1.327044
width= 400ft/ 1.327044= 301.42 ft

The perimeter would be
perimeter: 2(length+width)
perimeter: 2(400ft +301.42ft)= 1402.84ft   ---> might be rounded into 1400ft

Answer 2

tan(a)= opposite/adjacent Here, a is 53 degrees, opposite is the long side of the playground (400 feet), and adjacent is the short side of the playground (unknown). tan(53 degrees)=400/x x=400/tan(53 degrees) x=301.4 feet The perimeter is twice the length of the short side plus twice the length of the long side. p=2*400+2*301.4 Perimeter is 1402.8 feet