The quadrilateral ABCD has area of 58 in2 and diagonal AC = 14.5 in. Find the length of diagonal BD if AC ⊥ BD.

Question

The quadrilateral ABCD has area of 58 in2 and diagonal AC = 14.5 in. Find the length of diagonal BD if AC ⊥ BD.

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Verity 4 years 2021-08-29T05:44:14+00:00 1 Answers 35 views 0

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  1. Neala
    0
    2021-08-29T05:46:11+00:00
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    Answer:

    (look in the the Step by step)

    Step-by-step explanation:

    When the diagonals of a quadrilateral are perpendicular, the area of that quadrilateral is half the product of their lengths.

    .. A = (1/2)*d₁*d₂

    Substituting the given information, this becomes

    .. 58 in² = (1/2)*(14.5 in)*d₂

    .. 2*58/14.5 in = d₂ = 8 in

    The length of diagonal BD is 8 in.

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