# Heron kills it

Geometry Level 5

A triangle with sides of $$\sqrt{a^2+16b^2}$$, $$\sqrt{9a^2+4b^2}$$, and $$2\sqrt{a^2+b^2}$$ such that $$a$$ and $$b$$ are positive integers with area $$30$$ is given. Find the number of ordered pairs $$(a,b)$$ that satisfy this restriction.

×