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

Oct 31, 2016

$8 \sqrt{2}$

#### Explanation:

Given a right-angled triangle with sides A,B, and C, and A is the hypotenuse,

$\implies {A}^{2} = {B}^{2} + {C}^{2}$
$\implies {A}^{2} = {B}^{2} + {7}^{2}$
$\implies B = \sqrt{{9}^{2} - {7}^{2}} = \sqrt{32} = \sqrt{16 \cdot 2} = 4 \sqrt{2}$

given the side length of the rectangle adjacent to side B $= 2$,
$\implies$ rectangle area $= 4 \sqrt{2} \cdot 2 = 8 \sqrt{2} = 11.31$