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

Sep 29, 2017

Area of rectangle = 11.4

#### Explanation:

Side A = 9/8; Side C = 3/5
Side B $= \sqrt{{A}^{2} - {C}^{2}} = \sqrt{{\left(\frac{9}{8}\right)}^{2} - {\left(\frac{3}{5}\right)}^{2}}$
${B}^{2} = {\left(\frac{9}{8}\right)}^{2} - {\left(\frac{3}{5}\right)}^{2}$
${B}^{2} = \frac{\left(81 \cdot 25\right) - \left(9 \cdot 64\right)}{64 \cdot 25}$
${B}^{2} = \frac{2025 - 576}{1600}$
${B}^{2} = \frac{1449}{1600}$
$B = \sqrt{\frac{1449}{1600}} = \frac{38.07}{40} = 0.95$
Area of the rectangle $= \left(0.95\right) \cdot 12 = 11.4$