   SEARCH HOME Math Central Quandaries & Queries  Question from Hunter, a student: The three sides of a right-angled triangle measure x-1, x+6, and 2x+1 in length. What are the possible lengths of the hypotenuse? Hi Hunter,
Thank-you for your question, I hope this helps.
We know that when solving right angle triangles, Pythagoras' Theorem comes in handy: If c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides then

a2 + b2 = c2

Since the lengths of the sides of a triangle are positive, x - 1 > 0 and thus x > 1 so in particular x is positive. Thus x - 1 is the length of the shortest side and it can't be the hypotenuse (as the hypotenuse is always the longest side).
If the hypotenuse has length 2x + 1 then we get;

(x-1)2 + (x+6)2 = (2x+1)2

What if the hypotenuse has length x + 6?

Hope this helps to get you started.

Melanie an Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.