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In quadrilateral ABCD above, what is the length of AB ?
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04 Jun 2020, 08:46
04 Jun 2020, 08:46
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Question Stats:
75% (00:45) correct
24% (00:48) wrong based on 45 sessions
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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. \(3\sqrt{3}\)
Re: In quadrilateral ABCD above, what is the length of AB ?
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04 Jun 2020, 08:46
04 Jun 2020, 08:46
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Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: In quadrilateral ABCD above, what is the length of AB ?
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04 Jun 2020, 09:02
04 Jun 2020, 09:02
1
Carcass 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. \(3\sqrt{3}\)
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
