# Issue with a right-angled triangle

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?

• Is the question worth to be unanswered? – tonny Nov 12 '14 at 9:55
• You introduced a variable $x$ that represents half the shorter side of the triangle. You calculated it correctly. What does the book say $x$ represents? Possibly they used it differently than you. Nothing in the problem mentions $x$, so if I introduce it as a symbol I can make it anything I like. – David K Nov 19 '14 at 3:54