# 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 , 3/5 , and 7 , respectively. What is the rectangle's area?

Dec 3, 2017

The area of the rectangle is 12.46 square units

#### Explanation:

The area of the rectangle is the product of the lengths of two sides.

One side is given as 7; the other side is B, the length of one leg of the right triangle.

So Area equals 7 times B
$A = 7 \times B$

First find B

The Pythagorean Theorem for this triangle is
${A}^{2} = {B}^{2} + {C}^{2}$
where A is the hypotenuse and C is one of the legs

Sub in the numerical values and solve for B.

. . A^2 . . = B ^2 + . .C ^2
((15)/(8))^2 = B ^2 + ((3)/(5))^2

1) Clear the parentheses by squaring the fractions

(225) / (64) = B ^2 + (9)/(25)

2) Subtract $\frac{9}{25}$ from both sides to isolate B ^2

(225) / (64) - (9)/25 = B ^2

3) Give the fractions a common denominator

(225*25 - 9*64) / (64*25) = B ^2

(5625 - 576) / (1600) = B ^2

(5049)/(1600) = B ^2

3.156 = B ^2

4) Find the square roots of both sides

$1.78 = B$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Now you can find the Area.

It is B $\times 7$

$7 \times 1.78 = 12.46$ $\leftarrow$ answer