# 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 15 , 1 , and 4 , respectively. What is the rectangle's area?

Mar 20, 2016

≈ 59.87 square units

#### Explanation:

The area of the rectangle = 4B . To calculate the value , requires knowing the value of B.
Since the triangle is right we can find B, using$\textcolor{b l u e}{\text{ Pythagoras' theorem }}$

The hypotenuse is A hence : ${A}^{2} = {B}^{2} + {C}^{2}$

and ${B}^{2} = {A}^{2} - {C}^{2} = {15}^{2} - {1}^{2} = 224$

now ${B}^{2} = 224 \Rightarrow B = \sqrt{224}$

and area of rectangle = 4B =  4xxsqrt224 ≈ 59.87