The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The area of the resulting rectangle is $90 ft^2$ . What is the original area of the square?

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Answer 1 · 2015-11-15T03:03:49

$A = 64 ft^2$

Let $x$ be the length of one side of the square

$A_r = LW$
$L = x + 7$
$W = x - 2$

$(x + 7)(x - 2) = 90$

$=> x^2 + 5x - 14 = 90$

$=> x^2 + 5x - 104 = 0$

$=> (x + 13)(x - 8) = 0$

$=> x = -13, x = 8$

But since we're dealing with measurements here, the value should be positive.

$x = 8$

$A_s = S^2$

$=> A_s = x^2$

$=> A_s = 8^2$

$=> A_s = 64$

The dimensions of a square are altered so that one dimension is increased by 7 feet, while the other is decreased by 2 feet. The area of the resulting rectangle is 90 ft^290 ft^2. What is the original area of the square?