# 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 18 , 5 , and 3 , respectively. What is the rectangle's area?

Apr 18, 2016

≈ 51.87 square units

#### Explanation:

The area of the rectangle = 3B

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

$\Rightarrow {A}^{2} = {B}^{2} + {C}^{2} \Rightarrow {B}^{2} = {A}^{2} - {C}^{2}$

here A = 18 , C = 5

$\Rightarrow {B}^{2} = {18}^{2} - {5}^{2} = 324 - 25 = 299$

now  B^2 = 299 rArr B = sqrt299 ≈ 17.29

area of rectangle $= 3 B = 3 \times 17.29 = 51.87$