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.

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- Mar 23rd 2011, 11:27 AMWilmerGeometric puzzle funCode:
`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. - Mar 30th 2011, 09:26 AMWilmer
Hint: CE = 19

- Jun 4th 2011, 11:35 AMCorpsecreate
can this really be solved without guessing values?

- Jun 4th 2011, 12:22 PMWilmer
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!):

__Spoiler__: