The length of a side of an equilateral triangle is x-4.5. First express it's perimeter as a sum. Next express its perimeter as a product. Explain why the two expressions are equvalent.

The sides of an equilateral triangle are same. So if one of the sides is (x-4.5), all the sides are (x-4.5).

Let the sides are a = (x-4.5), b = (x-4.5), c = (x-4.5)

1. Perimeter (as sum) = a+b+c

= (x-4.5) + (x-4.5) + (x-4.5)

= x+x+x-4.5-4.5-4.5

= 3x - 13.5

2. Perimeter (as product) = 3*a

= 3 * (x-4.5)

= 3*x - 3*4.5

= 3x - 13.5

(you can write 3*b or 3*c also as a=b=c.)

Both perimeter as sum and perimeter as product are same as adding a number three times is the same as multiplying it by 3.