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In this example, we're asked to use similar triangles
to determine the link of the missing side. The missing side is
X set up the proportions in as many ways as possible
and show the results are all the same. So when we're looking at similar triangles we
want to
set up a ratio of
side links of one triangle to
side links of the other triangle. So here's one way we could set this up,
we can set this up as X/12
equals 5/4.
We could also go
this way. That would be
X/9 equals
5/3. Now
I could also go backwards,
12/X then that would equal
4/5. we ccould go backwards the other way
9/X equals
3/5. Doesn't really matter as long as you're
consistent and there are actually four
other ways to set up these similar triangles that are correct
and we'll go over those at the end of the example.
So let's see if we can use the information in these proportions to
solve for x
X here is going to be 5 times 12
divided by 4, that's
60/4 which is
15. Here X
equals 5 times 9 divided by 3,
45/3 is 15. All of these Xs
should be 15. Here we have 5 times 12 so
60=4x, and we're using the cross product
method here. Divide both sides by 4
so 15=X. Here
9 times 5, 45 equals
X times 3, 3x. Divide both sides by 3
again X=15.
Let's see what the four other ways
I could set this up. I could actually go across
triangles. So if I said X/5,
then I would say equals 12/4
and
then I could say 5/X
equals 4/12.
I could also say that
X/5 equals
9/3 or
5/X equals
3/ and you should work these out
to verify for yourself that all the Xs
equal 15. So just in these
two similar triangles, finding one
unknown, there are eight different ways to set up the problem
correctly. There's about a thousand different ways
to set up the problem incorrectly. So when you're setting up your similar
triangles,
be sure that you're working with the same
proportions as you're setting up your
numerator and denominator of your fraction. So
X is to 12 as 5 is to 4
and that gives you the correct proportion, same for all of these.