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 5 , respectively. What is the rectangle's area?

Apr 3, 2016

≈ 40.31 square units

Explanation:

The area of the rectangle $\textcolor{b l u e}{\text{ = 5B }}$

Require to find B. Since it is a right triangle we can use$\textcolor{red}{\text{ Pythagoras' theorem }}$

Since side A is the hypotenuse then ${A}^{2} = {B}^{2} + {C}^{2}$

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

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

so area of rectangle = 5B = 5xxsqrt65 ≈ 40.31" square units "