Math CentralQuandaries & 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

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS