Which length is the geometric mean between x and c?

Question

anonymous · Answer

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anonymous · Answer

A. b
B. h
C. a
D. y

mathstudent55 · Answer

The Right Triangle Altitude Theorem
Part A: The length of the altitude drawn to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

mathstudent55 · Answer

Part B: If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

anonymous · Answer

I'm lost.

mathstudent55 · Answer

The answer to this question comes form the theorem above.
The theorem has two parts.
In part A, the length of the altitude is the geometric mean of the two segments of the hypotenuse. That is the geometric mean of x and y. That's not what you are asked.
So let's look at part B.

anonymous · Answer

Okay.

mathstudent55 · Answer

In part B, each leg of the right triangle is the geometric mean of the entire hypotenuse and the segment of the hypotenuse near that leg.
In your case, c is the entire hyoptenuse.
x is the segment of the hypotenuse near leg a.

anonymous · Answer

is it given that you have a right triangle?

mathstudent55 · Answer

Since you have x and c, it looks like part B of the theorem is being used.

anonymous · Answer

Yes, it is given.|dw:1375467681521:dw|

mathstudent55 · Answer

The answer is the leg closer to x.

anonymous · Answer

The leg closer to x....so uhm...a?

anonymous · Answer

No wait...is it y?

mathstudent55 · Answer

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