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21 August, 07:56

The square below has an area of

64

-

16

x

+

x

2

64-16x+x

2

64, minus, 16, x, plus, x, squared square meters.

What expression represents the length of one side of the square?

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Answers (1)
  1. 21 August, 08:06
    0
    8-x meters

    Step-by-step explanation:

    Both 64 and x^2 are perfect squares, since 64 = (8) ^2 and x^2 = (x) ^2.

    Additionally, 16x is twice the product of the roots of 64 and x^2, since 16x=2 (8) (x).

    So we can use h the square of a difference pattern to factor:

    a^2-2 (a) (b) + b^2 = (a-b) ^2

    In this case, a=8 and b=x:

    (8) ^2-2 (8) (x) + (x) ^2 = (8-x) ^2

    In conclusion ...

    64-16x+x^2 = (8-x) ^2

    So the side length of the square is 8-x meters.
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