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 `7`, `2`, and `9`, respectively. What is the rectangle's area?

Answer 1

≈ 60.374 square units

Explanation:

The area of the rectangle = 9B , where B has to be found.

Since the triangle is right , with A the hypotenuse , we can find B using `color(blue)" Pythagoras' theorem "`

then : `A^2 = B^2 + C^2 rArr B^2 = A^2 - C^2`

`B^2 = 7^2 - 2^2 = 49 - 4 = 45`

now `B^2 = 45 rArr B = sqrt45`

and area of rectangle = 9B = `9xxsqrt45 ≈ 60.374`