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.

Without loss of generality let us label the smallest side of the triangle a, the second smallest/largest side a+r, and the largest side (a+2r). Then the perimeter is 3*(a+r), and the corresponding equilateral triangle has sides of s=(a+r) and thus area of √3s²/4 = √3(a+r)²/4.

Posted by Hal9000 on 2003-11-23 14:19:48