Question

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of `15/8`, `3/5`, and `6`, respectively. What is the rectangle's area?

Answer 1

`(9sqrt(561))/20`

Explanation:

Side `B` has length given by applying Pythagoras theorem:

`B = sqrt(A^2-C^2)`

`color(white)(B) = sqrt((15/8)^2-(3/5)^2)`

`color(white)(B) = sqrt(225/64-9/25)`

`color(white)(B) = sqrt(5049/1600)`

`color(white)(B) = (3sqrt(561))/40`

So the area of the rectangle is:

`6B = (18sqrt(561))/40 = (9sqrt(561))/20`