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18 February, 10:21

one diagonal of a rhombus is tree times long as the other diagonal if the area of the rhombus is 54 square millimeters what is the length of the diagonals

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  1. 18 February, 13:04
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    The length of the diagonals are 6mm and 18mm

    Step-by-step explanation:

    In this question, we are tasked with calculating the lengths of the diagonals of a rhombus, given the area of the rhombus and how the two diagonals differ from each other.

    Mathematically, for a rhombus, we can calculate the area of the rhombus using the formula.

    A = 1/2 * d1 * d2

    We are also told in the question that one diagonal is there times longer than the other.

    So we can say that d1 = 3d2

    hence our A becomes;

    A = 1/2 * 3d2 * d2

    For clarity sake, let's call d2 d only

    Hence

    54 = 1/2 * 3d * d

    3d^2 = 108

    d^2 = 108/3

    d^2 = 36

    d = square root of 36

    d = + 6 or - 6

    we ignore - 6 as lengthy cannot be negative

    hence d = d2 = 6mm

    But d1 = 3d2

    d1 = 3 * 6 = 18mm
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