The sides of a triangle are in arithmetic progression and its area is 3/5th the area of an equilateral triangle with the same perimeter.

Find the ratio of the sides of the triangle.

(In reply to re(3): Starters- self correction by drew)

This one would be nearly impossible to solve without Heron's formula, I think, because the perimeter, the sides, and the area need to be related by some formula in order to get the result. For the record, Heron's formula for the area of a triangle with sides a,b,c is

A=sqrt(s*(s-a)*(s-b)*(s-c))

where s=(a+b+c)/2 (the semiperimeter).

An equilateral triangle of side 1 has area (sqrt(3)/2)*1/2 by height*base/2. By Heron, the same area is
sqrt(3/2*1/2*1/2*1/2), so the formula checks for equilateral triangles.

Posted by Richard on 2003-11-23 15:19:54