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.

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

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