# 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 4 , 2 , and 9 , respectively. What is the rectangle's area?

Mar 5, 2016

Area of a rectangle is $18 \sqrt{3}$

#### Explanation:

Hypotenuse $A = 4$.
Cathetus $C = 2$.
Cathetus $B$ is not given.
By Pythagorean Theorem ${B}^{2} + {C}^{2} = {A}^{2}$
Therefore, $B = \sqrt{{4}^{2} - {2}^{2}} = 2 \sqrt{3}$
The rectangle, built on cathetus $B$, has sides $2 \sqrt{3}$ and $9$.
Therefore, its area is $2 \sqrt{3} \cdot 9 = 18 \sqrt{3}$.