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30 May, 01:29

The perimeter of a quadrilateral (four-sided polygon) is 58 inches. The longest side is three times as long as the shortest side. The other two sides are equally long and are 5 inches longer than the shortest side. Find the length of all four sides.

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  1. 30 May, 03:30
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    Step-by-step explanation:

    From an algebraic perspective.

    polygon had four sides.

    perimeter (sides added together) = 58inches.

    longest side + shortest side + (shortest side + 5) + (shortest side + 5) = 58

    let shortest side be s

    3s + s + (s + 5) + (s + 5) = 58

    4s + (s + 5) + (s + 5) = 58

    6s + 10 = 58

    6s = 58 - 10

    6s = 48

    s = 48 : 6

    s = 8

    Therefore,

    longest side = 3 (shortest side)

    longest side = 3 (8)

    longest side = 24 inches

    shortest side = 8 inches

    the other two sides are equal

    side = shortest side + 5

    side = 8 + 5

    side = 13 inches

    *To confirm answer

    add all sides together to get back the perimeter.

    longest side + shortest side + side + side = perimeter

    24 + 8 + 13 + 13 = 58
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