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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 D2 = L2 + W2. In this case, D = 5, and L = W + 1. Substituting the known values into the formula results in 52 = (W + 1)2 + W2.
25 = (W + 1)(W + 1) + W2
25 = W2 + 2W + 1 + W2
25 = 2W2 + 2W + 1 (Note: This equation is a quadratic equation and can be solved by setting it equal to zero and factoring.)
0 = 2W2 + 2W – 24
1/2(0) = 1/2(2W2 + 2W – 24)
0 = W2 + W – 12
0 = (W – 3)(W + 4)
W – 3 = 0 OR W + 4 = 0
W = 3 OR W = –4 (not a possible solution)