The three sides of an equilateral triangle are increased by 20cm, 30cm, and 40cm, respectively. The resulting triangle's perimeter is between twice and three times the perimeter of the original triangle. What can you conclude about the length of the side ofthe original triangle?

Question

pfenn1 · Answer

Can you write an equation for the resulting perimeter of the triangle if you assume x = length of the side of the original equilateral triangle?

anonymous · Answer

I don't understand?

pfenn1 · Answer

What is the equation for the perimeter of a triangle?

anonymous · Answer

x+x+x ?

pfenn1 · Answer

Correct.  So the perimeter of the new triangle (where the three sides are increased by 20cm, 30cm, and 40cm, respectively) is given by what equation?

anonymous · Answer

(x+20) + (x+30) + (x+40) ?

pfenn1 · Answer

Correct.

pfenn1 · Answer

The resulting triangle's perimeter is between twice and three times the perimeter of the original triangle.  So if P1 is the original perimeter and P2 is the perimeter of the resultant triangle then $$2P _{1}\le P _{2}\le3P _{1}$$  Substitute in the values for P1 and P2 in terms of x

pfenn1 · Answer

$$P_1=x+x+x=3x$$$$P_2=(x+20)+(x+30)+(x+40)=3x+90$$

anonymous · Answer

How do I solve that as an inequality?

pfenn1 · Answer

You can solve them independently.  $$6x \le 3x+90 \le 9x$$$$3x+90 \ge 6x$$and $$3x+90 \le 9x$$

pfenn1 · Answer

Do you know how to do this?

anonymous · Answer

Yes, I do. 
The answer I got was X is between 15 and 30. Is that correct?

pfenn1 · Answer

Yep.  Great!

anonymous · Answer

Thank you so much!!

pfenn1 · Answer

You are so welcome!