# Thread: Pythagoras Problem

1. ## Pythagoras Problem

Hi all........new to the forum and straight in with a problem.

I have a problem that i assumed could be solved by Pythagoras theorem.

I know the length of the hypotenuse (22") and the ratio of lengths for the catheti (16:10)

Please can anyone let me know if this is possible?

Graham

2. Originally Posted by GrahamV
Hi all........new to the forum and straight in with a problem.

I have a problem that i assumed could be solved by Pythagoras theorem.

I know the length of the hypotenuse (22") and the ratio of lengths for the catheti (16:10)

Please can anyone let me know if this is possible?

Yes, it is possible! If the two sides are in ratio $\displaystyle \frac{16}{10}$ then, taking y to be the longer of the two sides, $\displaystyle \frac{x}{y}= \frac{10}{16}$ so that $\displaystyle x= \frac{10}{16}y= \frac{5}{8} y$.
Putting that into the Pythagorean formula, $\displaystyle x^2+ y^2=$$\displaystyle \left(\frac{5}{8}y\right)^2+ y^2= 22^2$. That gives you a simple equation to solve for y and then use $\displaystyle x= \frac{5}{8}y$ to find x.