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Mathematicsresear

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## Homework Statement

Find the known pythagorean triangles with sides of integers lengths, given the area of the pythagorean triangle is 60.

## Homework Equations

Pythagorean triangles are right angled triangles.

a primitive pythagorean triple is of the form:

x=2mn

y=m^2-n^2

z=m^2+n^2

gcd(m,n)=1 so one is even and the other is odd.[/B]

## The Attempt at a Solution

xy=120 so d^2ab =120

( d I x = a , d I y = b)[/B]

the only possible values for d^2 are 1 and 4

so I have two cases:

1) ab = 120

2) ab=30

I can now write a = 2mn

b= m^2-n^2

so mn(m^2-n^2)=15

mn(m-n)(m+n)=15

I am unsure as what to do next.