# 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 13 , respectively. What is the rectangle's area?

Feb 9, 2018

Area of rectangle $\approx 120$

#### Explanation:

Given:
In triangle $A B C$
$A$ is hypotenuse = 11
$C$ = 6
So, B is the other side of the right angled triangle.
Let us find B using Pythagoras theorem:

$\implies {A}^{2} = {B}^{2} + {C}^{2}$

$\implies {B}^{2} = {A}^{2} - {C}^{2}$

$\implies {B}^{2} = {11}^{2} - {6}^{2}$

$\implies {B}^{2} = 121 - 36 = 85$

$\implies B = \sqrt{85}$

$\implies B \approx 9.22$

Also given the length of side of rectangle adjacent to B = 13

$\implies$ sides of rectangle are B =9.22 and adjacent side =13.
So, area of rectangle will be:

$\therefore A r e a = 9.22 \times 13 = 119.86 \approx 120$