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10 July, 01:12

Two regular octagons have areas of 48 mm² and x² + 8x mm². What values of x make the octagons congruent?

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  1. 10 July, 02:00
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    4 and

    -12

    Explanation

    The octagons can be considered congruent when their areas are the same.

    That is:

    48 mm² = x² + 8x mm²

    x² + 8x = 48

    x² + 8x + 4² = 48 + 4²

    (x + 4) ² = 48 + 16

    = 64

    x + 4 = √64 or x + 4 = - √64

    x = 8 - 4 x = - 8 - 4

    = 4 = - 12
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