# 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 14 , 3 , and 14 , respectively. What is the rectangle's area?

Aug 6, 2018

$A = 28 \sqrt{46}$

#### Explanation:

*not drawn to scale

So this is what is given to us in the problem

First, we want to solve for the third side of the triangle using the Pythagorean Theorem - ${a}^{2} + {b}^{2} = {c}^{2}$

In this case, it can be confusing since, in the problem, Side A is the hypotenuse, but in the theorem, $c$ is always the hypotenuse

We can plug the values into the theorem, note that the 3 can be used as $a$ or $b$ in the theorem
${3}^{2} + {b}^{2} = {14}^{2}$
${b}^{2} = 184$
$b = \sqrt{184}$

Now that we have the third side of the triangle, we know its the same as the other side of the rectangle since it shares this side

Now to find the area we can $l \cdot w$

$A = 14 \cdot \sqrt{184} = 14 \sqrt{184}$

We can simplify it to $28 \sqrt{46}$