if each side of a square is increased by 6, the area is multiplied by 16

Question

if each side of a square is increased by 6, the area is multiplied by 16

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Melanie 2 weeks 2021-09-12T22:52:38+00:00 1 Answer 0

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    2021-09-12T22:54:35+00:00

    Answer:

    The original side length is 2. The area of the original square is 4.

    This means the new side length, x+6, would be 8. The area of the new square is 64.

    Step-by-step explanation:

    If you want to know what the length of the side is, here is how you solve it:

    x is the side length

    therefore, x^{2} is the area

    if x+6 becomes the length and the area of this is 16x^{2}

    then we can say that (x+6)^{2} = 16x^{2}

    we can expand this to become x^{2} + 12x +36=16x^{2}

    which becomes -15x^{2} +12x +36=0

    If we factor it, we get (-15x^{2} + 30x)(-18x+36)=0

    -15x(x-2)-18(x-2)=0

    (-15x-18)(x-2)=0

    x=2\\or\x=-\frac{6}{5}

    because length cannot be a negative number, the only option for the original side length is 2. The area of the original square is 4.

    This means the new side length, x+6, would be 8. The area of the new square is 64.

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45:7+7-4:2-5:5*4+35:2 =? ( )