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Question:

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

A
3 inches

Explaination

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)