# 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 18 , 15 , and 9 , respectively. What is the rectangle's area?

Jan 19, 2017

Area of rectangle is $89.56$.

#### Explanation:

In the right angled triangle, as $A = 18$ is hypotenuse and $C = 15$, we have side $B$ given by Pythagoras theorem as

$\sqrt{{18}^{2} - {15}^{2}} = \sqrt{324 - 225} = \sqrt{99} = 3 \sqrt{11}$

We have rectangle adjacent to side $B$, hence one side of rectangle is $3 \sqrt{11}$ and as other side of rectangle is $9$

Hence area of rectangle is

$9 \times 3 \sqrt{11} = 27 \times 3.317 = 89.559 \approx 89.56$.