For the area of the deck to be doubled, he should increase each dimension by 3.
The deck is 4 feet by 21 feet.
She wants to increase each dimension by equal lengths so that its area is doubled.
Therefore,
initial area = 4 × 21 = 84 ft²
Hence,
The increase by equal length
width = x + 4
length = x + 21
area = 2(84) = 168 ft²
Therefore,
(x + 4)(x + 21) = 168
x² + 21x + 4x + 84 = 168
x² + 25x + 84 = 168
x² + 25x + 84 - 168 = 0
x² + 25x - 84 = 0
(x + 28) • (x - 3) = 0
x = -28 or 3
It can only be positive.
Therefore, she should increase each dimension by 3.
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