# 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 4 , 2 , and 5 , respectively. What is the rectangle's area?

Dec 22, 2017

Area of rectangle is $17.32$ sq.unit.

#### Explanation:

Hypotenuse A=4 ; C=2 and adjacent to side $B$, the

side of rectangle $D = 5$

We know in a right triangle A^2=B^2+C^2; A=4 ,C=2

$\therefore {4}^{2} = {B}^{2} + {2}^{2} \mathmr{and} {B}^{2} = 16 - 4 = 12 \therefore B = \sqrt{12} = 2 \sqrt{3}$

Area of rectangle is A_r=B*D ; D=5:. A_r=2sqrt3*5

$\therefore {A}_{r} = 10 \sqrt{3} \approx 17.32 \left(2 \mathrm{dp}\right)$ sq.unit.

Area of rectangle is $17.32$ sq.unit. [Ans]