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 10 , 8 , and 16 , respectively. What is the rectangle's area?

Mar 4, 2016

The area of the rectangle is $96 {\text{ units}}^{2}$.

Explanation:

Your triangle and rectangle should look like this:

Let's compute the length of the side $B$ first.

As it is one of the sides of a right triangle, this can be done with Pythagorean Theorem:

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

$\implies {8}^{2} + {B}^{2} = {10}^{2}$

$\implies 64 + {B}^{2} = 100$

$\implies {B}^{2} = 36$

$\implies B = 6$

So now we know the length of two adjacent sides of a rectangle $B = 6$ and $D = 16$ and we can compute the area of the rectangle:

${\text{Area" = B * D = 6 * 16 = 96 " units}}^{2}$