Two angles of a triangle are 45º each and its longest side is 12cm, this simply describes an isosceles triangle two equal angles and two equal sides using Pythagoras theorem, \(x^2 + x^2 = 12^2\) \(2x^2\) = 144 \(x^2\) = 72( after dividing b/sides by 2) x = \(\sqrt{72} = 6\sqrt{2}\)cm.