Question 529691
An athletic club has 225 feet of fencing to enclose a tennis court. What quadratic function can be used to find the maximum area of the tennis court? Find the maximum area and the lengths of the resulting fence.
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let x=length
let y=width
2x+2y=perimeter=225
2y=225-2x
y=(225-2x)/2=112.5-x
area=x*y=x(112.5-x)=(112.5x-x^2)
area=-x^2+112.5x
complete the square
area=-(x^2+112.5x+3164.06)+3164.06
area=-(x+56.25)^2+3164.06
ans:
area≈3164 sq ft
length≈56.25 ft
width=112.5-56.25≈56.25 ft