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In quadrilateral ABCD above, what is the length of AB ?
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26 Apr 2019, 01:38
26 Apr 2019, 01:38
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A
B
C
D
E
Difficulty:
5%
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Question Stats:
87% (01:09) correct
13%
(01:30)
wrong
based on 1745
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In quadrilateral ABCD above, what is the length of AB ?
A. \(\sqrt{26}\)
B. \(2\sqrt{5}\)
C. \(2\sqrt{6}\)
D. \(3\sqrt{2}\)
E. \(3\sqrt{3}\)
PS58502.01
OG2020 NEW QUESTION
Attachment:
2019-04-26_1235.png [ 8.99 KiB | Viewed 34445 times ]
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In quadrilateral ABCD above, what is the length of AB ?
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Updated on: 20 May 2020, 11:18
Updated on: 20 May 2020, 11:18
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Top Contributor
Bunuel wrote:
In quadrilateral ABCD above, what is the length of AB ?
A. \(\sqrt{26}\)
B. \(2\sqrt{5}\)
C. \(2\sqrt{6}\)
D. \(3\sqrt{2}\)
E. \(3\sqrt{3}\)
PS58502.01
OG2020 NEW QUESTION
Attachment:
2019-04-26_1235.png
First add a line to join B and D:
If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem.
Either way, we'll see that the triangle's hypotenuse (BD) must have length 5
Now, when we focus on the red right triangle, we can . . .
. . . apply the Pythagorean Theorem to write: x² + 1² = 5²
Simplify: x² + 1 = 25
So: x² = 24
So: x = √24 = √[(4)(6)] = (√4)(√6) = 2√6
Answer: C
Cheers,
Brent
Originally posted by BrentGMATPrepNow on 29 Apr 2019, 10:49.
Last edited by BrentGMATPrepNow on 20 May 2020, 11:18, edited 1 time in total.
Last edited by BrentGMATPrepNow on 20 May 2020, 11:18, edited 1 time in total.
General Discussion
In quadrilateral ABCD above, what is the length of AB ?
[#permalink]
Updated on: 05 Aug 2019, 15:31
Updated on: 05 Aug 2019, 15:31
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Join D and B
DCB is an right angle triangle
\(DB^2= CD^2 +BC^2\)
\(DB^2=9 +16=25\)
\(or DB=5\)
Also, \(DB^2= AB^2 + AD^2\)
\(25=AB^2 + 1\)
\(AB^2 = 24\)
\(AB= 2\sqrt{6}\)
DCB is an right angle triangle
\(DB^2= CD^2 +BC^2\)
\(DB^2=9 +16=25\)
\(or DB=5\)
Also, \(DB^2= AB^2 + AD^2\)
\(25=AB^2 + 1\)
\(AB^2 = 24\)
\(AB= 2\sqrt{6}\)
