# 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 15/8 , 3/5 , and 6 , respectively. What is the rectangle's area?

Mar 8, 2017

$\frac{9 \sqrt{561}}{20}$

#### Explanation:

Side $B$ has length given by applying Pythagoras theorem:

$B = \sqrt{{A}^{2} - {C}^{2}}$

$\textcolor{w h i t e}{B} = \sqrt{{\left(\frac{15}{8}\right)}^{2} - {\left(\frac{3}{5}\right)}^{2}}$

$\textcolor{w h i t e}{B} = \sqrt{\frac{225}{64} - \frac{9}{25}}$

$\textcolor{w h i t e}{B} = \sqrt{\frac{5049}{1600}}$

$\textcolor{w h i t e}{B} = \frac{3 \sqrt{561}}{40}$

So the area of the rectangle is:

$6 B = \frac{18 \sqrt{561}}{40} = \frac{9 \sqrt{561}}{20}$