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.

area of triange with sides x-y,x,x+y:
(3/16x^4-12/16x^2*y^2)^(1/2)
area of equallateral triangle with side x:
(3/16x^4)^(1/2)

(3x^4-12x^2*y^2)^(1/2)=3/5(3x^4)^(1/2)
3x^4-12x^2*y^2=27/25*x^4
x^2-4y^2=9/25*x^2
y^2=4/25*x^2
y=2/5*x

The ratio of the sides with x=5 is 3:5:7

Posted by Katie on 2003-11-28 15:30:33