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4 May, 15:42

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.

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  1. 4 May, 17:45
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    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.
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