Triangle ABC has integer sides: perimeter = 96Code:C B D E A
CD bisects angle ACB ; CE is a median (thus BE = AE).
CD and CE both have integer lengths.
Find the triangle's sides, plus CD and CE.
Well, you're given the perimeter=96 :
so "find" a triangle with integer sides and perimeter = 96 : very few!
With sides = a>b>c :
bisector from C = sqrt[ab(1 - k)] where k = c^2 / (a+b)^2
median from C = sqrt[2(a^2 + b^2) - c^2] / 2
And I gave median = 19 as clue...so not too difficult to wrap up.
I'll post/hide the solution (in case I forget!):