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Question:

# A rectangle is one inch longer than it is wide. Its diagonal is five inches. What’s the width of the rectangle?

A 3 inches.
explanation

The diagonal formula for a rectangle is $D^2 = L^2 + W^2$. In this case, D = 5, and L = W + 1. Substituting the known values into the formula results in $5^2 = (W+1)^2 + W^2$
$25 = (W+1)(W+1) + W^2$
$25 = W^2 + 2W +1 + W^2$
$25 = 2W^2 + 2W +1$
(Note: This equation is a quadratic equation and can be solved by setting it equal to zero and factoring.)
$0 = 2W^2 + 2W - 24$
$1/2(0) = 1/2(2W^2 + 2W - 24)$
$0 = W^2 + W - 12$
$0 = (W - 3) + (W + 4)$
$W - 3 = 0$ or $W + 4 = 0$
$W = 3$ or $W = -4$ (not a possible solution)

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