# 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 6 , 2 , and 4 , respectively. What is the rectangle's area?

Jun 8, 2017

Area of rectangle is $16 \sqrt{2}$ sq.unit.

#### Explanation:

The sides of right triangle are hypotenuse ,A=6 ,C=2 ; B= ?

We know ${A}^{2} = {B}^{2} + {C}^{2} \therefore {B}^{2} = {A}^{2} - {C}^{2} = 36 - 4 = 32 \therefore B = \sqrt{32} = 4 \sqrt{2}$

Now we have two adjacent sides of rectangle as $B = 4 \sqrt{2} \mathmr{and} D = 4$

Area of rectangle is ${A}_{r} = B \cdot D = 4 \sqrt{2} \cdot 4 = 16 \sqrt{2}$ sq.unit [Ans]