What is value of X in given figure.

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.

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

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