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805+ (Hard)|   Geometry|      
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figjam786
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What is value of X in given figure. 21 Jul 2022, 08:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

0% (00:00) correct 100% (01:46) wrong based on 16 sessions

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Date
Time
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Not Attempted Yet
What is value of \(X\) in given figure.


a) 7
b) 8
c) \(\sqrt{71}\)
d) \(\sqrt{80}\)
e) 9
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C

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ksyed
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What is value of X in given figure. 22 Jul 2022, 08:51
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How could the answer be C, please explain?
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What is value of X in given figure. 22 Jul 2022, 09:08
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How could the answer be C, please explain?
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ThatDudeKnows > can u help?

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ThatDudeKnows
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What is value of X in given figure. Updated on: 22 Jul 2022, 11:19
Originally posted by ThatDudeKnows on 22 Jul 2022, 09:24.
Last edited by ThatDudeKnows on 22 Jul 2022, 11:19, edited 5 times in total.
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figjam786
What is value of \(X\) in given figure.


a) 7
b) 8
c) \(\sqrt{71}\)
d) \(\sqrt{80}\)
e) 9
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figjam786
ksyed
Mohammadmo

I think the first instinct is to sketch in a couple extra lines as in the attached figure. But once you do that, you can see that by labeling one of the angles a and the complementary angle b, you end up with two 3-4-5 triangles, one of which has the 3 opposite angle a and the other of which has the 4 opposite angle a. We can't do that! So, we know that the figure is drawn out of scale and that point at the bottom middle is NOT actually on a horizontal line created by making a rectangle!

I've redrawn the figure closer to scale and added a few extra points and lines.

Looking at triangle ACF, we have
\(4^2 + 8^2 = AC^2\)
\(16 + 64 = AC^2\)
\(80 = AC^2\)
\(AC = \sqrt{80}\)

Now looking at triangle ABC, we have
\(3^2 + AB^2 = \sqrt{80}^2\)
\(9 + AB^2 = 80\)
\(AB^2 = 71\)
\(AB = \sqrt{71}\)

Answer choice C.
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Mohammadmo
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What is value of X in given figure. 22 Jul 2022, 10:11
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I don't understand why the answer is not 9 ?!

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