## Geometric triangles

### Problem 370

Published on Sunday, 5th February 2012, 07:00 am; Solved by 324; Difficulty rating: 65%Let us define a *geometric triangle* as an integer sided triangle with sides `a` ≤ `b` ≤ `c` so that its sides form a **geometric progression**, i.e. `b ^{2}` =

`a`·

`c`.

An example of such a geometric triangle is the triangle with sides `a` = 144, `b` = 156 and `c` = 169.

There are 861805 geometric triangles with perimeter ≤ 10^{6} .

How many geometric triangles exist with perimeter ≤ 2.5·10^{13} ?