Question 818187: Triangles PQR and XYZ are similar. If and what is the PQ=6,PR=4,XY=9and what is the length of side XZ ? Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! In similar triangles the corresponding sides are proportional. But what sides correspond to each other?
A statement of similarity tells use what corresponds to what. "Triangles PQR and XYZ are similar" tells us that P corresponds to X (because they are the first letters in the names), that Q corresponds to Y (because they are the second letters) and R corresponds to Z (because they are the last letters. From this we also know that PQ corresponds to XY and PR corresponds to XZ.
So a proportion the three sides we know and the one side we want to know is:
Substituting in the values for the known lengths:
Now we solve. I like to reduce fractions first:
Now we can cross-multiply. Or ... we could take advantage of some simple logic: The second numerator is exactly twice the first numerator. This means that the second denominator must be twice the first denominator. So XZ = 6. (This is the same answer you get if you cross-multiply.)
P.S. Cross-multiplying works on all proportions. The shortcut we used at the end does not always work as it did here. For example:
11 is not a well-known multiple of 3 so it will be difficult to figure out how many times 7 x is. So we should probably use cross-multiplying to solve this one.
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