# 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 , 1 , and 15 , respectively. What is the rectangle's area?

May 1, 2016

≈ 103.92 square units

#### Explanation:

The area of the rectangle = 15B

To calculate the value we require to find length of B.

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

For this triangle ${A}^{2} = {B}^{2} + {C}^{2}$

$\Rightarrow {B}^{2} = {A}^{2} - {C}^{2} = {7}^{2} - {1}^{2} = 48$

now ${B}^{2} = 48 \Rightarrow B = \sqrt{48} = \sqrt{16 \times 3} = 4 \sqrt{3}$

hence area of rectangle= 15B=15xx4sqrt3=60sqrt3 ≈ 103.92