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a rectangle of perimeter 100 units has the dimensions shown. Its area is given by the function A = w(50 - w). What is the GREATEST area such a rectangle can have?
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a rectangle of perimeter 100 units has the dimensions shown. Its area is given by the function A = w(50 - w). What is the GREATEST area such a rectangle can have?

User Dave Sherohman
by
7.3k points

1 Answer

3 votes
P = 2 W + 2 L
100 = 2 W + 2 L /:2
50 = W + L
A = W ( 50 - W ) = 50 W - W²
A` (W) = 50 - 2 W
50 - 2 W = 0
2 W = 50
W = 50 : 2
W = 25; L = 50 - 25 = 25
The greatest area such a rectangle can have:
A = 25 * 25 = 625 units²
User Ilia Maskov
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7.9k points
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