Pythagoras Problem

**GrahamV** · January 28th 2010, 04:23 AM

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?

thanks in advance

Graham

**HallsofIvy** · January 28th 2010, 04:41 AM

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?

thanks in advance

Graham

Yes, it is possible! If the two sides are in ratio $\frac{16}{10}$ then, taking y to be the longer of the two sides, $\frac{x}{y}= \frac{10}{16}$ so that $x= \frac{10}{16}y= \frac{5}{8} y$ .

Putting that into the Pythagorean formula, $x^2+ y^2=$ $\left(\frac{5}{8}y\right)^2+ y^2= 22^2$ . That gives you a simple equation to solve for y and then use $x= \frac{5}{8}y$ to find x.

**GrahamV** · January 28th 2010, 05:48 AM

That's brilliant.......Thanks for the quick response

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