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1 March, 18:20

At one show he places three mirrors: A, B and C, in a right triangular form. If the distance between A and B is 15 more than the distance between A and C, and the distance between B and C is 15 less than the distance between A and C. What is the distance between mirror A and mirror C?

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  1. 1 March, 18:34
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    60

    Step-by-step explanation:

    We have the following sides:

    AB, AC, BC

    By means of the statement we know that:

    The distance between A and B is 15 more than the distance between A and C, that is:

    AB = AC + 15

    The distance between B and C is 15 less than the distance between A and C

    BC = AC - 15

    We can infer that the longest side is AB, therefore being right triangular form, we have to:

    AC ^ 2 + BC ^ 2 = AB ^ 2

    Replacing we have:

    AC ^ 2 = AB ^ 2 - BC ^ 2

    AC ^ 2 = (AC + 15) ^ 2 - (AC - 15) ^ 2

    AC ^ 2 = (AC ^ 2 + 30 * AC + 225) - (AC ^ 2 - 30 * AC + 225)

    AC ^ 2 = 60 * AC

    AC = 60

    Which means that the distance between mirror A and C is 60.

    To check, we have:

    AB = (60 ^ 2 + 45 ^ 2) ^ (1/2) = (5625) ^ (1/2) = 75

    AB = AC + 15 = 60 + 15 = 75
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