A childs rectangular play area is bordered on one side by a house and on the other three sides by 40 meters of rope. Find the max area of the playground.

Question

 P= 40m

Answer 1

let x be width and y the length

P= 2y + x=40

so x= 40-2y

A=xy=y(40-2y)=40y-2y^2

dA/Dy=40-4y=0

so y=10 and x=20

max area = 200 sq m^2