# 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 17 , 2 , and 9 , respectively. What is the rectangle's area?

Feb 29, 2016

Area = (Aproximately) $151.9$ sq.units

#### Explanation:

From the diagram (and using the Pythagorean Theorem)
$\textcolor{w h i t e}{\text{XXX}} B = \sqrt{{A}^{2} - {C}^{2}}$
$\textcolor{w h i t e}{\text{XXXX}} = \sqrt{{17}^{2} - {2}^{2}}$
$\textcolor{w h i t e}{\text{XXXX}} = \sqrt{285}$
and using a calculator
$\textcolor{w h i t e}{\text{XXXX}} \approx 16.88$

The Area of the Rectangle is
$\textcolor{w h i t e}{\text{XXX}} B \times 9 \approx 16.88 \times 9 \approx 151.9$