All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Sides Of A Triangle (Posted on 2003-11-23)
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.)
 Starters | Comment 4 of 14 |
Call the three sides x-y, x, and x+y.

Using Heron's formula, the area of the triangle is:
√((3x/2)(3x/2-x+y)(3x/2-x)(3x/2-x-y))=
√((3x²/4)(x²/4-y²))=
√(3x^4/16-3x²y²/4)

The area of the equilateral triangle is:
x²√3/4

Putting this together:
x²√3/4=(3/5)*√(3x^4/16-3x²y²/4)
5x²√3/12=√(3x^4/16-3x²y²/4)
75x^4/144=3x^4/16-3x²y²/4
48x^4/144+3x²y²/4=0
x²(x²/3+3y²/4)=0
So, either x=0(obviously not forming a triangle), or x²/3+3y²/4=0

Would anyone like to check my work or finish it?
 Posted by Tristan on 2003-11-23 12:22:33

 Search: Search body:
Forums (0)