# 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 5 , 4 , and 11 , respectively. What is the rectangle's area?

Mar 6, 2017

The area of the rectangle is $33$.

#### Explanation:

From the data given we can draw the following shape:

Since the triangle is right angled, we can determine the length of B using the Pythagorean theorem.

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

${B}^{2} + {4}^{2} = {5}^{2}$

${B}^{2} + 16 = 25$

Subtract $16$ from each side.

${B}^{2} = 25 - 16$

${B}^{2} = 9$

Determine the square root.

$B = 3$

Since we know that $B = 3$ and that the side adjacent to $B$ is $11$, the area of the rectangle can be calculated using the formula:

$A = l \times h$

where $l =$length ($11$) and $h =$height (in this case: $B = 11$)

$A = 3 \times 11$

$A = 33$