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Math Help - Parallelogram Problems

  1. #1
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    Exclamation Parallelogram Problems

    In a parallelogram ABCD, AB=15 cm and BC = 14cm. The foot H of the perpendicular dropped from Bto ADis between A and D. Find the length of the diagonal BD if BH= 12cm,

    I will be amazed at whoever can do this

    thanks-a-million
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  2. #2
    MHF Contributor
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    Quote Originally Posted by googa View Post
    In a parallelogram ABCD, AB=15 cm and BC = 14cm. The foot H of the perpendicular dropped from Bto ADis between A and D. Find the length of the diagonal BD if BH= 12cm,

    I will be amazed at whoever can do this

    thanks-a-million
    In the right triangle BHA:
    By Pythagorean theorem,
    AH = sqrt(15^2 -12^2) = sqrt(81) = 9 cm

    So, in the right triangle BHD:
    HD = 14 -9 = 5 cm
    Thus,
    BD = sqrt(5^2 +12^2) = sqrt(169) = 13 cm ----------answer
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