Question

A rectangle is 1 inch longer than it is wide. Its diagonal is 5 inches. What's the width of the rectangle?

Answer 1

The width is 4 inches

Explanation:

Represent the length and width by L and W respectively. Then L = W + 1.

According to the Pythagorean Theorem, the diagonal length is

D = sqrt( [W]^2 + [W + 1}^2 ) = 5, or [W]^2 + [W + 1}^2 = 25.

Then W^2 + W^2 + 2W + 1 = 25, and 2W^2 + 2W - 24 = 0.

Reducing, we get W^2 + W - 12 = 0, or (W + 4)(W - 4) = 0. Then W - 4 = 0, and W (the width) is 4. Then L = 5.

The width is 4 inches.

Answer 2

Ok so the length of the triangle is x+1, and the diagonal is 5. Using Pythagorean’s theorem, the answer should be both -4 and 3