# 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 11 , 6 , and 12 , respectively. What is the rectangle's area?

Nov 30, 2016

Rectangle's area is $110.64$.

#### Explanation:

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 $11$, $6$ and $12$ respectively.

The figure appears as one shown below.

We can find the length of $B$ using Pythagoras theorem and using this we have ${A}^{2} = {B}^{2} + {C}^{2}$ or ${B}^{2} = {A}^{2} - {C}^{2} = 121 - 36 = 85$ and hence

$B = \sqrt{85} = 9.22$

And rectangle's area is $9.22 \times 12 = 110.64$