# 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 , 12 , and 9 , respectively. What is the rectangle's area?

Mar 10, 2016

6sqrt5 ≈ 120.75 " square units "

#### Explanation:

area of rectangle = length$\times \text{ breadth } = 9 B$
and require to find B.

Since right triangle can use$\textcolor{b l u e}{\text{ Pythagoras's theorem }}$

then ${A}^{2} = {B}^{2} + {C}^{2}$

hence ${B}^{2} = {A}^{2} - {C}^{2} = {18}^{2} - {12}^{2} = 180$

since ${B}^{2} = 180 \Rightarrow B = \sqrt{180} = 6 \sqrt{5}$

thus area of rectangle = 9sqrt180 ≈ 120.75 " square units "