SOLUTION: Find the maximum area of a rectangle whose perimeter is 18 inches.

Question 774482: Find the maximum area of a rectangle whose perimeter is 18 inches.
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
Q:
Find the maximum area of a rectangle whose perimeter is 18 inches.
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A:
Let x be the length and y be the width of a rectangle.
Perimeter, P = 2x + 2y = 18
So x + y = 9 or y = 9 - x
Area, A = xy = x(9 - x)
A =
A is a quadratic function.
A has a maximum value because the coefficient of is negative.
To get the maximum value, we compute the vertex (h,k) where h = and k = .
In , a = -1, b = 9, and c = 0.
So h = = = is the length.
and k = = is the area.
Therefore the maximum area of a rectangle is square inches.
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