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:

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

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