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Find the maximum area for a rectangle with a perimeter of 120 meters.

User Atul N
by
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1 Answer

7 votes

Answer:

900 m^2

Explanation:

Let x = length, y = width

perimeter = 2x + 2y = 2(x + y) = 120. so

x + y = 60, or y = 60 - x

Area = xy = x(60 - x) = 60x - x^2

= -(x^2 - 60x + 30^2) + 30^2

= 900 - (x - 30)^2

Note (x - 30)^2 is never negative, at least zero.

When (x - 30) = 0, the area is the largest which is 900 m^2

User Czchlong
by
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