# 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 , 4 , and 12 , respectively. What is the rectangle's area?

May 7, 2016

≈ 68.93 square units

#### Explanation:

Here is a sketch (not to scale)

The area of the rectangle = 12B

To calculate the area we require to know the value of B.

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

The hypotenuse is A hence ${A}^{2} = {B}^{2} + {C}^{2}$

and rearranging we get

${B}^{2} = {A}^{2} - {C}^{2} = {7}^{2} - {4}^{2} = 33$

now ${B}^{2} = 33 \Rightarrow B = \sqrt{33}$

area of rectangle =12B=12xxsqrt33 ≈ 68.93" square units "