Question

9. The diagonal of a rectangle is 25 in. The width is 15 in. What is the length?

Answer 1

Hello! Your answer is 20 in.

Pythagorean's theorem states that with a right triangle, $a^{2} + b^{2} = c^{2}$ when a and b are the two sides that form a 90 degree angle, and c is the third side.

In this case, c = 25, and a = 15. We are looking for b. This is because the width and length form a 90 degree angle, so the width and length are a and b, meaning that c must be the diagonal. The diagonal is 25 in, so c = 25, and the width is 15, so either a or b is equal to 15. I just went with a = 15.

Now, substitute these values into the formula.

$a^{2} + b^{2} = c^{2}$

$15^{2} + b^{2} = 25^{2}$

$225 + b^{2} = 625$

$b^{2} = 400$

$b = \sqrt{400}$

$b = 20$

Therefore, the length = 20, or the length = 20 inches.

Hope this helps!