# 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 12 , 3 , and 5 , respectively. What is the rectangle's area?

Mar 10, 2016

≈ 58.095 square units

#### Explanation:

The area of the rectangle = 5B (lengthxx " breadth ")

To find B use $\textcolor{b l u e}{\text{ Pythagoras' theorem }}$

since A is the hypotenuse then ${A}^{2} = {B}^{2} + {C}^{2}$

hence ${12}^{2} = {B}^{2} + {3}^{2} \Rightarrow {B}^{2} = {12}^{2} - {3}^{2} = 135$

now ${B}^{2} = 135 \Rightarrow B = \sqrt{135}$

thus area of rectangle  = 5sqrt135 ≈ 58.095 " square units "