Question

help please will fan and medal

Answer 1

questions here.

Answer 2

@Mythorius

Answer 3

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Answer 4

so.. hmm have you covered similarities yet?

Answer 5

yes

Answer 6

ok...gimme a sec... lemme post a pic

Answer 7

ok

Answer 8

hmmm actually

Answer 9

shoot... anyhow... lemme not post the pic just yet

instead... notice yours

the hypotenuse is 18 long
one part of that is 9

well, 9 is half 18, so that means the "upper" part is also 9

Answer 10

so... you see what kind of triangle that is?

Answer 11

yeah

Answer 12

so, tis a 45-45-90 triangle
meaning that, if you draw an "angle bisector" down from the vertex of the altitude
it will simply make another two small 45-45-90 triangles

Answer 13

so.. if you squeeze out one of the smaller triangles made by that angle bisector
we have say let us use the top smaller triangle
so

Answer 14

thie issue with a "geometric mean" is that, when you draw a line from the the 90 degree angle, down to the bottom perpendicularly, you end up with two smaller triangles that are similar to the bigger one

notice the picture here, like so

in your case, or in the case of a 45-45-90 triangle
it does the same, but, the two smaller similar triangles, are, well, 45-45-90 also :)

Answer 15

ok

Answer 16

so... using the 45-45-90 rule
notice yours, "x" is 9, thus "z" is \(\bf 9\sqrt{2}\)