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

Apr 8, 2016

24 square units

Explanation:

The area of the rectangle = $\textcolor{b l u e}{\text{ 4B}}$

To calculate the value of the area , require to find B.

Since the triangle is right with hypotenuse A , we can use $\textcolor{red}{\text{ Pythagoras' theorem " " to find B}}$

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

$\Rightarrow {B}^{2} = {10}^{2} - {8}^{2} = 100 - 64 = 36$

now ${B}^{2} = 36 \Rightarrow B = \sqrt{36} = 6$

and area of rectangle = 4B $= 4 \times 6 = 24 \text{ square units }$