What is value of X in given figure.

Question

What is value of  X  in given figure.

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

ksyed · Answer

How could the answer be C, please explain?

figjam786 · Answer

ThatDudeKnows  > can u help?

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ThatDudeKnows · Answer

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.

Mohammadmo · Answer

I don't understand why the answer is not 9 ?!

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What is value of X in given figure.

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What is value of X in given figure.

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