Pythagorean Triples

Question

So I'm trying to recall the following: can you deduce that a triangle is a Pythagorean Triple (PT) based on only the hypotenuse? Ex. If we know it's a right triangle, and are given the hypotenuse 5, can we assume that the legs are 3 and 4?

I know this doesn't work the other way around, meaning if we knew it was a right triangle, and was only given a leg of 3, we couldn't assume it was a PT. Is it a different case for a hypotenuse though?

Would appreciate any help, as well as a link to where you might have found your explanation.

Bunuel · Answer

Knowing that hypotenuse equals to 5 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 3:4:5. Or in other words: if a^2+b^2=5^2 DOES NOT mean that a=3 and b=4 , certainly this is one of the possibilities but definitely not the only one. In fact a^2+b^2=5^2 has infinitely many solutions for a and b and only one of them is a=3 and b=4 . For example: a=1 and b=\sqrt{24} or a=2 and b=\sqrt{21} ... Check Triangles chapter of Math Book for more: math-triangles-87197.html Hope it's clear.

KarishmaB · Answer

I will add one more point here: Pythagorean triplets represent the right triangle with integral sides. So if you know the hypotenuse is 5 and the other 2 sides are integers too, then the other two sides must be 3 and 4. Else, they could be anything. Check out this wikipedia link for more: https://en.wikipedia.org/wiki/Pythagorea ... an_triples

TBT · Answer

If the same question is given but we are provided the other 2 sides are integers, then 3 4 5 can be concluded or triplet can be used directly without need of anything else?

Pythagorean Triples

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards