# 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 3 , 2 , and 22 , respectively. What is the rectangle's area?

Oct 10, 2016

$22 \sqrt{5}$

#### Explanation:

Let's write what we know of the triangle
A=3
C=2

Since its a right triangle and A is the hypotenuse, we can apply Pythagoras' Theorem, so:
${A}^{2} = {B}^{2} + {C}^{2}$
${3}^{2} = {B}^{2} + {2}^{2}$
${B}^{2} = 9 - 4$
$B = \sqrt{5}$

Now for the rectangle.
Its sides are B and 22 and its areas is B*22. Since $B = \sqrt{5}$, the area of the rectangle is $\textcolor{b l u e}{22 \sqrt{5}}$