An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle.

Question

anonymous · Answer

Do you have its illustrated picture, Ducky?

anonymous · Answer

I'm afraid not; the text is all we have to go on.

anonymous · Answer

It's not right triangle?

anonymous · Answer

No, the triangle type isn't specified.

anonymous · Answer

Many thanks!

anonymous · Answer

Because the bisector line in this case ISN'T perpendicular with base, apply golden rule:

 a/5 = ( a + 5)/ a
->a² = 5 (a +5)
->a² - 5a -25 = 0
=> a = (+5 ± √125 )/ 2 = 8.1