# 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 9/8 , 3/5 , and 15 , respectively. What is the rectangle's area?

Nov 10, 2016

Area of rectangle is $7.8$

#### Explanation:

As hypotenuse $A$ of $\Delta A B C$ is $\frac{9}{8}$ and one side $C$ is $\frac{3}{5}$

third side $B = \sqrt{{\left(\frac{9}{8}\right)}^{2} - {\left(\frac{3}{5}\right)}^{2}} = \sqrt{\frac{81}{64} + \frac{9}{25}}$

= $\sqrt{1.265625 - 0.36} = \sqrt{0.905625} = 0.952$

As $B$ is one side of rectangle and other side is $15$

Area of rectangle is $15 \times 0.952 = 7.8$