# 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 2 , 1/3 , and 3 , respectively. What is the rectangle's area?

Mar 15, 2016

sqrt35 ≈ 5.916" square units "

#### Explanation:

The area of the rectangle = 3B . To calculate this area , require to find length of B.
Since this is a right triangle , B can be found using $\textcolor{b l u e}{\text{ Pythagoras' theorem }}$

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

thus ${B}^{2} = {A}^{2} - {C}^{2}$

here A = 3 and C $= \frac{1}{3}$

hence :${B}^{2} = {2}^{2} - {\left(\frac{1}{3}\right)}^{2} = 4 - \frac{1}{9} = \frac{35}{9}$

now ${B}^{2} = \frac{35}{9} \Rightarrow B = \sqrt{\frac{35}{9}} = \frac{1}{3} \sqrt{35}$

area of rectangle = 3B =  3xx1/3 sqrt35 = sqrt35 ≈ 5.916