Question

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.

Answer 1

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.