Mathematics

Question

In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.

1 Answer

  • Answer:

    AC = 14 sqrt(2) = 19.80    

    Step-by-step explanation:

    Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

    Givens

    • <ABC = <ACD                          
    • ABCD  is a trapezoid
    • BC = 14
    • AD = 28
    • AC is a transversal of BC and AD

    Solution

    • <ABC = <ACD                Given
    • <DAC = <ACB                Alternate interior angles.
    • ΔACB ≅ΔDAC               AA
    • <BAC = <ADC                Angles of similar triangles are equal
    • AC /28 = 14/AC              Form a proportion from corresponding sides
    • AC*AC = 14 * 28             Cross multiply the proportion. Combine
    • AC^2 = 392                    Express as prime factors.
    • AC^2 = 7*7*2*2*2           Take the square root of both sides
    • sqrt(AC)^2 = sqrt(7*7*2*2*2)
    • AC = 7*2 * sqrt(2)
    • AC = 14 sqrt(2) = 19.80    

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