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22 September, 02:36

The length of a diagonal of a square is 37√2 millimeters. find the perimeter of the square

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  1. 22 September, 03:34
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    The answer is 148.

    Step-by-step explanation:

    Because it is a square, the sides are equal. Taking half the square, you have a right triangle with sides that are equal with a hypotenuse of 37√2.

    The equation a^2 + b^2 = c^2 applies.

    In this case sides a and b are equal, so we can substitute a for b. The following equation applies:

    a^2 + a^2 = c^2

    2a^2 = c^2

    Substitute in the value of C:

    2a^2 = (37√2) ^2

    2a^2 = 1369 * 2

    Divide both sides by 2

    a^2 = 1369

    Take the square root of both sides:

    a = 37

    Each side is 37 units. The perimeter is 37 * 4 = 148 units.
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