# 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 9 , 4 , and 8 , respectively. What is the rectangle's area?

Mar 5, 2016

8sqrt65 ≈ 64.5 " square units"

#### Explanation:

To calculate the area of the rectangle , we require to find the length of side B . This can be done using$\textcolor{b l u e}{\text{ Pythagoras's theorem }}$

In the right triangle: ${A}^{2} = {B}^{2} + {C}^{2}$

hence ${B}^{2} = {A}^{2} - {C}^{2} = {9}^{2} - {4}^{2} = 81 - 16 = 65$

now ${B}^{2} = 65 \Rightarrow B = \sqrt{65}$

thus area of rectangle = 8xxsqrt65 = 8sqrt65 ≈ 64.5