The area of a triangle ABC is 5cm

^{2}.

AB=2cm and BC=5cm.

How much is AC?

No calculators, please..

(In reply to

Solution by Kenny M)

While perhaps trivial, this occurred to me: given a and b and Area and then asked to find c would have yielded two answers, had not Area = 1/2 a b. That the area is maximized with a right angle, and so gives a single answer, is proven by differentiation:

Area = 1/2 a b sin_theta

d_Area/d_sin_theta = 0

gives theta = 90.

For smaller Areas, the two sin_theta solutions are the acute and obtuse angles on either side of 90, and had Area been greater than 1/2 a b, there'd be no answer at all.

*Edited on ***March 6, 2021, 6:27 pm**