# 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 7 , 2 , and 8 , respectively. What is the rectangle's area?

Oct 9, 2017

$A r e {a}_{\text{rectangle}} = 24 \sqrt{5} \approx 53.67$

#### Explanation:

Draw the figure to better understand the problem:

To find the area of the rectangle, find the side length of B first.

Use the pythagorean theorem:

${B}^{2} + {2}^{2} = {7}^{2}$

${B}^{2} = {7}^{2} - {2}^{2}$
${B}^{2} = 49 - 4 = 45$
$B = \sqrt{45}$

$B = 3 \sqrt{5}$
$\text{ } B \approx 6.71$

$A r e {a}_{\text{rectangle}} = 8 \cdot 3 \sqrt{5}$

$A r e {a}_{\text{rectangle}} = 24 \sqrt{5} \approx 53.67$