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The figure shows a quadrangle ABCD with AB = 3,

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The figure shows a quadrangle ABCD with AB = 3,

by Max@Math Revolution » Tue May 05, 2020 6:24 pm

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[GMAT math practice question]

The figure shows a quadrangle ABCD with AB = 3, AD = 5 and CD = 6. The diagonals AC and BD are perpendicular to each other. What is the length of BC?
5.5ps.png
A. \(\sqrt{3}\)
B. 4
C. 2 \(\sqrt{5}\)
D. 3\(\sqrt{3}\)
E. 3 \(\sqrt{5}\)
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Re: The figure shows a quadrangle ABCD with AB = 3,

by Max@Math Revolution » Wed May 06, 2020 11:51 pm
=>
5.5ps(a).png
Assume BC = x and P is the intersection of AC and BD.
Then AP^2 + DP^2 = 25, BP^2 + CP^2 = x^2 and we add those two equations and have AP^2 + BP^2 + CP^2 + DP^2 = x^2 + 25.
And AP^2 + BP^2 = 9 and CP^2 + DP^2 = 36 and we add those two equations and have AP^2 + BP^2 + CP^2 + DP^2 = 45.
Thus, we have x^2 + 25 = 45 or x^2 = 20.
Then we have x = 2 √5, and the answer is C.

Answer: C
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