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By similarity properties, the shortest and longest sides of two similar triangles correspond to each other.
See solution.
We were given a triangle XYZ.
| Side of △ XYZ | Corresponds to |
|---|---|
| Shortest side of △ XYZ (10) | Shortest side of △ ABC (l_1) |
| Longest side of △ XYZ (13) | Longest side of △ ABC (l_2) |
| Third side of △ XYZ (12) | Third side of △ ABC (l_3) |
We have three ways to find the scale factor.
On the other hand, if we are given one side of △ ABC — let's say AB — but we are not told which side is (l_1, l_2, or l_3), then we will not know which correspondence to use and we can get an incorrect scale factor. k_1 = AB/10 or k_2 = AB/13 or k_3 =AB/12 That is why we needed to know which side is 20 units long — so that we found the correct corresponding scale factor and then the length of the other two sides.