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 = √(400)`

`b = 20`

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

Hope this helps!