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 `9`, `4`, and `5`, respectively. What is the rectangle's area?

Answer 1

≈ 40.31 square units

Explanation:

The area of the rectangle `color(blue)" = 5B "`

Require to find B. Since it is a right triangle we can use`color(red)" Pythagoras' theorem "`

Since side A is the hypotenuse then `A^2 = B^2 + C^2`

and `B^2 = A^2 - C^2 = 9^2 - 4^2 = 81 - 16 = 65`

now `B^2 = 65 rArr B = sqrt65`

so area of rectangle = 5B = `5xxsqrt65 ≈ 40.31" square units "`