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*(sa)*(sb)*(sc))
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 20031123 15:19:54 