# 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?

##### 1 Answer

Mar 4, 2016

The area of the rectangle is

#### Explanation:

Your triangle and rectangle should look like this:

Let's compute the length of the side

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

#C^2 + B^2 = A^2#

#=> 8^2 + B^2 = 10^2#

#=> 64 + B^2 = 100#

#=> B^2 = 36#

#=> B = 6#

So now we know the length of two adjacent sides of a rectangle

#"Area" = B * D = 6 * 16 = 96 " units"^2#