A school is fencing in a rectangular area for a playground. It plans to enclose the playground using fencing on three sides (the fourth is a wall) . The school has budgeted enough money for 75 ft of fencing material and would like to make a playground with an area of 600 ft^2. Solve for the width of the fence by "completing the square".

Question

A school is fencing in a rectangular area  for a playground. It plans to enclose the playground using fencing on three sides (the fourth is a wall) . The school has budgeted enough money for 75 ft of fencing material and would like to make a playground with an area of 600 ft^2. Solve for the width of the fence by "completing the square".

Reiny · Accepted Answer

let the width be x
let the length be y, along the wall

so 2x + y = 75
y = 75-2x

area = xy = 600
x(75 - 2x) = 600
-2x^2 + 75x = 600
x^2 - 37.5x = -300
x^2 - 37.5x + 351.5625 = -300 + 351.5625
(x - 18.75)^2 = 51.5625
x - 18.75 = appr 7.18

x = appr 25.93
y = 23.139

Rick · Answer

thnks man you helped me big time