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Sides Of A Triangle (Posted on 2003-11-23) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ravi Raja    
Rating: 4.1111 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): Starters- self correction | Comment 11 of 14 |
(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

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