# 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 , 5 , and 22 , respectively. What is the rectangle's area?

Jun 30, 2016

$22 \cdot \sqrt{56} \approx 164.6 s q u n i t$

#### Explanation:

Given
$A \to \text{Hypotenuse} = 9$
$C \to \text{Other side } = 5$

Applying Pythagorus theorem

$B = \sqrt{{A}^{2} - {C}^{2}} = \sqrt{{9}^{2} - {5}^{2}}$
$\implies B = \sqrt{56}$

The side of the rectangle adjacent to side B is 22.

So area of the rectangle
$= \sqrt{56} \times 22 \approx 164.6 s q u n i t$