# 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 4 , 6 , and 9 , respectively. What is the rectangle's area?

May 21, 2016

The given configuration can not exist. Please correct and re-submit.

#### Explanation:

The question claims that side A is the hypotenuse with a length of $4$. It is also claimed that side C of the same right triangle has a length of $6$.

The length of the hypotenuse of a right triangle must be greater than the length of either of the other sides.

Possible valid respective lengths:
$< A , C , \text{rectangle's side} > =$
$\textcolor{w h i t e}{\text{XXX}} < 6 , 4 , 9 >$, or
$\textcolor{w h i t e}{\text{XXX}} < 9 , 6 , 4 >$, or
$\textcolor{w h i t e}{\text{XXX}} < 9 , 4 , 6 >$

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Steps in solving this type of problem.

1. Use the Pythagorean Theorem to find the length of side B: $\sqrt{{A}^{2} - {C}^{2}}$
2. Rectangle's area $= B \times \text{rectangle's side}$