Question

Lenox wants to make an equilateral triangle with a perimeter of 3x+ 9. Is this possible? Why or why not?

Answer 1

For an equilateral triangle, all sides must have the same length. This means the perimeter must be evenly divisible by 3. If we can divide the expression above by 3 then the answer is yes it's possible:

$\frac{3x+9}{3} =\frac{3(x+3)}{3} =x+3$

We have just solved for the side length, and can see that the expression is evenly divisible by 3, so an equilateral triangle can be created using this expression for its perimeter by subbing in any whole number for x.