Thread: Length of a side

Hi,

I am looking for nudge in the right direction with this one. Very dense at the moment.

The Triangle XYZ is right-angled at Y and M is midpoint of XZ. Given that YZ = 5, and YM = 6.5 cm, find the length of XY.



What am I missing? I have a feeling that the M is midpoint part is crucial. But how?

Thanks for all your help!

Originally Posted by mathguy80

Hi,

I am looking for nudge in the right direction with this one. Very dense at the moment.

The Triangle XYZ is right-angled at Y and M is midpoint of XZ. Given that YZ = 5, and YM = 6.5 cm, find the length of XY.



What am I missing? I have a feeling that the M is midpoint part is crucial. But how?

Thanks for all your help!

Here is a hint: Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the vertices.

It then follows that XZ = 13 and so XY = 12 is easily obtained.

Fantastic! I completely blanked out on that. I have been using "Diameter subtends a right angle on circle", but didn't think of using it in reverse. Thanks a lot, a very elegant problem and solution.