# 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 10 , 3 , and 3 , respectively. What is the rectangle's area?

Feb 25, 2017

${\text{Area}}_{\square} = 3 \sqrt{91} \approx 28.62$ square units

#### Explanation:

Since $A , B , C$ are sides of a right triangle (with $A$ the hypotenuse), and
since $\left\mid A \right\mid = 10$ and $\left\mid C \right\mid = 3$
then by the Pythagorean Theorem
$\textcolor{w h i t e}{\text{XXX}} \left\mid B \right\mid = \sqrt{{10}^{2} - {3}^{2}} = \sqrt{91}$

Therefore the rectangle has sides with lengths $3$ and $\sqrt{91}$
and an area of $3 \times \sqrt{91} = 3 \sqrt{91}$
$\textcolor{w h i t e}{\text{XXX}}$or (using a calculator) approximately $28.62$