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

Mar 25, 2016

≈ 60.374 square units

#### Explanation:

The area of the rectangle = 9B , where B has to be found.

Since the triangle is right , with A the hypotenuse , we can find B using $\textcolor{b l u e}{\text{ Pythagoras' theorem }}$

then : ${A}^{2} = {B}^{2} + {C}^{2} \Rightarrow {B}^{2} = {A}^{2} - {C}^{2}$

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

now ${B}^{2} = 45 \Rightarrow B = \sqrt{45}$

and area of rectangle = 9B =  9xxsqrt45 ≈ 60.374