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?

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Answer 1 · 2016-03-04T09:22:54

The area of the rectangle is #96 " units"^2#.

Your triangle and rectangle should look like this:

enter image source here

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#

#=> 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 #B = 6# and #D = 16# and we can compute the area of the rectangle:

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