data/problems/176.yml
---
:id: 176
:name: Right-angled triangles that share a cathetus
:url: https://projecteuler.net/problem=176
:content: |+
The four right-angled triangles with sides (9,12,15), (12,16,20), (5,12,13) and (12,35,37) all have one of the shorter sides (catheti) equal to 12. It can be shown that no other integer sided right-angled triangle exists with one of the catheti equal to 12.
Find the smallest integer that can be the length of a cathetus of exactly 47547 different integer sided right-angled triangles.