The city put a fence around a playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the smallest perimeter for the area of 324 square yards.

One side is 15 yards longer than the other. Find the side lengths of the fence and the perimeter of the playground.

Question

The city put a fence around a playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the smallest perimeter for the area of 324 square yards.

One side is 15 yards longer than the other. Find the side lengths of the fence and the perimeter of the playground.

ilovecake · Answer

P = 2L + 2W 
L = 15 + W 
A = L * W = 324 

Plug in the value of L into the area formula 
A = (15 + W)(W) = 15W + W² = 324 or 
W² + 15W - 324 = 0 
Factor this equation to find (W - 12)(W + 27) = 0, which gives you a solution of W = 12 or W = -27. Since the width can't be negative, the Width of the playground is 12 yards, which gives you a length of 12 + 15 or 27 yards. Double check your answers to confirm. 12 x 27 = 324, so that matches. 

Now you know the length and width, so solve for the perimeter. :)

anonymous · Answer

thank ya @Ilovecake btw i love cake too haha

ilovecake · Answer

lol :) good luck