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Bunuel
In parallelogram ABCD below, what is the length of diagonal BD?


A. \(\sqrt{29}\)

B. \(2 \sqrt{29}\)

C. \(3 \sqrt{29}\)

D. \(4 \sqrt{29}\)

E. \(5 \sqrt{29}\)

Like the majority of geometry questions of all difficulty levels, let's just Ballpark!

The base is 12. How long is that diagonal? I don't know, let's say something close to 10? 11? Definitely less than 12 and definitely more than half of 12.

Look at the answer choices. \(\sqrt{29}\) is more than 5 and less than 6.
Answer choice A is less than 6.
Answer choices C, D, and E are all greater than 15.

Answer choice B.

Please, REASON through whether you need to do the math before you waste the time doing the math.

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why is BE 10 if AD is 12?
firas92
Let a perpendicular line from D, meet BC at E. Now we have DE=4, BE=10 and triangle BDE is a right angled triangle.

Now using pythagoras,

BD=√(10^2+4^2) = √116 = 2√29

Answer is (B)

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