+0  
 
0
95
3
avatar

In a right triangle, all the sides are positive integers.  One of the legs is equal to 180.  How many different possible values are there for the hypotenuse?

 Dec 7, 2020
 #1
avatar+323 
+2

The better question is, "How many pythagorean triples are there which have one of the legs as 180, but not the hypotenuse?"

 

There are up to two of them, I believe.

 

One I know is {19,180,181}. That's one...

 

We can plug 180 into the pythagorean triple finder, and there are a couple rules here: https://primes.utm.edu/glossary/page.php?sort=PrmPythagTriples#:~:text=The%20square%20of%20the%20length,5%2C12%2C13).

 

Play around with that a little and tell us what you find!

 Dec 8, 2020
 #2
avatar
+1

How about a few of them:

 

L      L    H

180 19 181
180 33 183
180 75 195
180 96 204
180 112 212
180 135 225
180 189 261
180 240 300
180 273 327
180 299 349
180 385 425
180 432 468
180 525 555
180 663 687
180 800 820
180 891 909
180 1344 1356
180 1615 1625
180 2021 2029
180 2697 2703

 Dec 8, 2020
 #3
avatar+323 
0

I was... not expecting that.

 

Can another answerer check that for me? I'm stumped here.

Nacirema  Dec 8, 2020

25 Online Users

avatar
avatar
avatar