# 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 15/8 , 4/5 , and 1 , respectively. What is the rectangle's area?

Sep 10, 2016

$A = 1.6958$

#### Explanation:

Knowing that the hypotenuse, $a = \frac{15}{8} \mathmr{and} c = \frac{4}{5}$, you can use Pythagoras' Theorem to find $b$

${b}^{2} = {a}^{2} - {c}^{2}$

${b}^{2} = {\left(\frac{15}{8}\right)}^{2} - {\left(\frac{4}{5}\right)}^{2} \text{ } \rightarrow {1.75}^{2} - {0.8}^{2}$

${b}^{2} = 2.875625$

$b = 1.6958$

Now that you have the length of $b$,

$A = l \times b$

$A = 1.6958 \times 1$

$A = 1.6958$