# 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 , 5 , and 22 , respectively. What is the rectangle's area?

Dec 5, 2017

The rectangle's area is $137.39$ sq.unit.

#### Explanation:

In right triangle hypotenuse $A = 8$ and one leg $C = 5$

We know in right triangle ${A}^{2} = {B}^{2} + {C}^{2} \therefore {B}^{2} = {A}^{2} - {C}^{2}$ or

${B}^{2} = \left(A + C\right) \left(A - C\right) \mathmr{and} {B}^{2} = \left(8 + 5\right) \left(8 - 5\right) = 39$

$\therefore B = \sqrt{39} \approx 6.245$. So in rectangle, adjacent sides are

$B \approx 6.245 \mathmr{and} D = 22$ . The area of rectangle is ${A}_{r} = B \cdot D$ or

${A}_{r} = 6.245 \cdot 22 \approx 137.39 \left(2 \mathrm{dp}\right)$ sq.unit

Rectangle's area is $137.39 \left(2 \mathrm{dp}\right)$ sq.unit [Ans]