# 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 8 , 2 , and 14 , respectively. What is the rectangle's area?

May 21, 2016

≈ 108.44 square units

#### Explanation:

Here is a sketch (not to scale)

Area of rectangle = 14B

To calculate this area we require to find B.

Since the triangle is right with hypotenuse A, then we can use
$\textcolor{b l u e}{\text{ Pythagoras' theorem"" to calculate B}}$

For the given triangle : ${A}^{2} = {B}^{2} + {C}^{2}$

$\Rightarrow {B}^{2} = {A}^{2} - {C}^{2} = {8}^{2} - {2}^{2} = 64 - 4 = 60$

now ${B}^{2} = 60 \Rightarrow B = \sqrt{60}$

area of rectangle=14B=14xxsqrt60≈108.44" square units"