https://pusd4237-phoenixunionhs-ccl.gradpoint.com/Resource/1726005,72F,0,0,0,0,0/Assets/testitemimages/geometry_a/similarity/mc078-1.jpg

When ya look at that pic, how do you find Y? How do you find X?

Question

https://pusd4237-phoenixunionhs-ccl.gradpoint.com/Resource/1726005,72F,0,0,0,0,0/Assets/testitemimages/geometry_a/similarity/mc078-1.jpg

When ya look at that pic, how do you find Y? How do you find X?

mertsj · Answer

Use this theorem:
 The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

anonymous · Answer

What's a geometric mean?

anonymous · Answer

Is it just a fancy way to say mean between hypotenuse X, 4, 12?

mertsj · Answer

yes

anonymous · Answer

So the geometric mean of the numbers in this problem = Y?

anonymous · Answer

geometric mean of a and b, if they are two real numbers is 

$$\Large \sqrt{a \times b}$$

anonymous · Answer

And that = Y?

anonymous · Answer

Nope, you have to use pythagoreans theorme to fin that value

mertsj · Answer

$$\frac{12}{y}=\frac{y}{4}$$

mertsj · Answer

$$y^2=48$$

mertsj · Answer

$$y=4\sqrt{3}$$

mertsj · Answer

Now use the Pythagorean Theorem to find x

anonymous · Answer

Ok, but what were those first two comments for in the problem?

anonymous · Answer

* Mertsj?

mertsj · Answer

I'm not sure what you are referring to.

anonymous · Answer

12/y=y/4-who, what where when why how? :(

mertsj · Answer

That's what the theorem means when it says that the altitude to the hypotenuse is the geometric mean of the segments of the hypotenuse.

anonymous · Answer

Oh, oh! Got it! Thanks!

mertsj · Answer

yw