# 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 16 , 4 , and 5 , respectively. What is the rectangle's area?

Apr 1, 2016

$20 \sqrt{15}$

#### Explanation:

Consider the diagram

Use the pythagorean theorem to find $c$

color(blue)(a^2+b^2=c^2

Where $c$ is the Hypotenuse and $a , b$ are the other two sides

$\rightarrow {4}^{2} + {b}^{2} = {16}^{2}$

$\rightarrow 16 + {b}^{2} = 256$

$\rightarrow {b}^{2} = 256 - 16$

$\rightarrow {b}^{2} = 240$

color(green)(rArrb=sqrt240=sqrt(16*15)=4sqrt15

Now we need to find the area of the rectangle,Use

color(blue)(Area=l*b

Where $l \mathmr{and} b$ are the sides of the rectangle

So,Area=

$\rightarrow 4 \sqrt{15} \cdot 5$

color(green)(rArr=20sqrt15