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Mathematics 33 Online
lexxii:

Find the value of Y

lexxii:

Shadow:

Do you know what geometric mean is?

lexxii:

No?

Shadow:

It's basically like similar triangles. Does that sound familiar?

lexxii:

Yes

Shadow:

|dw:1521405488658:dw| We basically want to be looking at that red line in the middle. We call that the altitude. In order to solve this triangle, we need to compare the knowledge that we know. Since these triangles share a side, we can do the following: \[\frac{ 9 }{ x } = \frac{ x }{ 3 }\] Where x is the length of the red line

Shadow:

Cross multiply \[x^2 = 27\] \[x = \sqrt 27 \] \[x = 3 \sqrt 3\] Now that we know the length of the red line, what can we do?

lexxii:

Use that to find the length of Y?

Shadow:

I shouldn't have used x as the variable for the side length xD But x in my work represents the altitude, or the red line in the drawing. We still need to find x and y for the problem, as shown in the image you shared. Now that we know the length of the altitude, what formula could we use to solve for x and y?

Shadow:

Haha, we would use Pythagorean's Theorem \[a^2 + b^2 = c^2\] Where 'a' and 'b' are the side lengths of a given triangle, and 'c' is the hypotenuse. Do you know how to use this formula?

lexxii:

\[a^2+b^2=c^2\] Yeah I do

lexxii:

So to find Y would you use \[9+3\sqrt{3}=Y\] ???

Shadow:

\[y^2 = 9^2 + (3 \sqrt 3)^2\]

lexxii:

So \[Y=6\sqrt{3}\]

lexxii:

Is that right?

Shadow:

That's what I got for y

Shadow:

What about for x?

lexxii:

So you would do \[x^2=3^2+(3\sqrt{3})\]

Shadow:

Don't forget the square on (3 sqrt 3)

lexxii:

Oh! I thought I did square it for some reason...?

lexxii:

So X would be 6?

Shadow:

That is what I got as well

lexxii:

Okay, thank you so much!

Shadow:

No problem

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