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 `3`, `2`, and `9`, respectively. What is the rectangle's area?

Answer 1

`9sqrt(5)` sq. units

Explanation:

By the Pythagorean Theorem:
`color(white)("XXX")B=sqrt(3^2-2^2)=sqrt(5)`

and therefore the area of the rectangle is
`color(white)("XXX")sqrt(5)xx9 = 9sqrt(5)`