+586 How many non-congruent right triangles are there, all of whose sides have positive integer lengths, and one of whose legs (i.e. not the hypotenuse) has length 162?
+129899 One place to start is to look at the divisors of 162 and see which ones are possible legs for "primitive" Pythagorean Triple right triangles
The divisors of 162 are 1 | 2 | 3 | 6 | 9 | 18 | 27 | 54 | 81 | 162
3 will work because 3-4-5 is a primitive triple
We need to divide 162 by each factor....and then multiply both 4 and 5 by this factor to find one triple
So
162/3 = 54
So 54 * 4 = 216
And 54 * 5 = 270
So 162 - 216 - 270 is a "triple"
And
9 will work because
9 - 40 - 41 is a primitive triple
So 162/9 = 18
And 18 * 40 = 720
And 18 * 41 = 738
So 162 - 720 - 738 is a "triple'
There are two more which are a lttle hard to find...the next is
27 - 364 - 365
So 162/27 = 6
And 364 * 6 = 2184
And 365 * 6 = 2190
So 162 - 2184 -2190 is a "triple'
The last is 162 - 6560- 6562
So....there are 4 which have one leg = 162
