The area of the right angle triangle is $18\text{ cm}^2$ and the ratio of its legs is $2:3$. What is the length of the hypotenuse?
I assumed the lengths of two sides to be $2x$ and $3x$. I used the formula for the area of a triangle and found out that $x=\sqrt{6}$ but my book says $x=6$, before using the Pythagorean theorem. Why is this?