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

Answer 1

63 square units

Explanation:

The area of the rectangle attached to B = 7B

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

`rArr A^2 = B^2 + C^2`

and : `B^2 = A^2 - C^2 = 15^2 - 12^2 = 81`

now `B^2 = 81 rArr B = sqrt81 = 9`

therefore area of rectangle = 7B =`7xx9 = 63" square units "`