# 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 3 , 2 , and 5 , respectively. What is the rectangle's area?

Mar 12, 2016

$A r e a = 5 \sqrt{5}$

#### Explanation:

Consider the diagram

We need to find the length $B$

$\therefore$ Use pythagorean theorem

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

Where

color(red)(c=Hypotencolor(red)(use

color(red)(a andb=other color(red)(two color(red)(sides

But, In this case $A$ is the $H y p o t e n$$u s e$

$\therefore {2}^{2} + {B}^{2} = {3}^{2}$

$\rightarrow 4 + {B}^{2} = 9$

$\rightarrow {B}^{2} = 9 - 4$

$\rightarrow {B}^{2} = 5$

$\Rightarrow B = \sqrt{5}$

We find that $B$ is one of the side of the rectangle

$A r e a$ $o f$ $r e c t a$$n g l$$e = l \cdot b$ $u n i t s$

color(green)( :.Area=sqrt5*5=5sqrt5