SOLUTION: Hi I need help with problem. I keep getting an impossible answer and i can't figure out what I'm doing wrong. This is the problem: The three sides of an equilateral triangle are in

Question 780019: Hi I need help with problem. I keep getting an impossible answer and i can't figure out what I'm doing wrong. This is the problem: The three sides of an equilateral triangle are increase by 20 cm, 30 cm, and 40 cm, respectively. The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle. What can you conclude about the length of a side of the original triangle?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The three sides of an equilateral triangle are increase by 20 cm, 30 cm, and 40 cm, respectively. The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle. What can you conclude about the length of a side of the original triangle?
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Let each side of the equilatera triangle be "x".
New sides are x+20, x+30, and x+40.
New perimeter is 3x+90
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Inequality:
2(3x) < 3x+90 < 3(3x)
6x < 3x+90 < 9x
---
3x < 90 < 6x
x < 30 < 2x
======
Each side of the orignal triangle is less than 30
================
Cheers,
Stan H.
================

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let the length of a side of the original triangle be

So new sides are ,,, and

The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle, or and
So

so and
So the side lengths of the original triangle are between and , or .

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