SOLUTION: solve for X <pre> ^ / \ 8/ \6

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Question 1109770: solve for X
                                 ^
                                / \
                              8/   \6
                              /     \
                             /       \
                            /____>____\
                           /           \
                          /             \
                       10/               \x
                        /                 \
                       /________>__________\

would it be 8/10=10/x or is it 8/6=10/x
Found 2 solutions by stanbon, greenestamps:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve for X
^
/ \
8/ \6
/ \
/ \
/____>____\
/ \
/ \
10/ \x
/ \
/________>__________\
would it be 8/10=10/x or is it 8/6=10/x
No. The top triangle is similar to the whole triangle
6/(6+x) = 8/(8+10)
6(18) = 8(6+x)
(3/4)18 = 6+x
x+6 = 13.5
x = 7.5
-------------
Cheers,
Stan H.
--------------------

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor seems to be saying that you have to use corresponding parts of the small triangle and the whole triangle to set up your proportion. While that is what seems obvious, since you are talking about similar triangles, it is possible to use parts of the triangles instead of the whole triangles.

Specifically, your proportion

8/6 = 10/x

is valid, because it compares corresponding parts -- even though the 10 and x are not parts of whole triangles.

Your other proportion, 8/10=10/x, is not valid because it does not compare corresponding parts.

So any one of these proportions could be used:
(8+10)/10 = (6+x)/x
(8+10)/8 = (6+x)/6
8/10 = 6/x
8/6 = 10/x

Clearly either of the last two is easier to use than either of the first two....