Question - Determining Scale Factor in Similar Triangles
Solution:
The given problem involves similar figures, specifically two triangles for which you must find the scale factor. To determine the scale factor from one triangle to another, you can divide a side length of one triangle by the corresponding side length of the other triangle.In the image, Triangle CDE with sides CD = 10, DE = 12, and CE = 16, and Triangle VUT with sides UV = 9.6 and UT = 12 are shown. Since the triangles are similar, their corresponding sides are proportional.We will take the side lengths of Triangle VUT and divide them by the corresponding sides of Triangle CDE to find the scale factor:VU (UV) / CD = 9.6 / 10 = 0.96UT / CE = 12 / 16 = 0.75As you can see, we got two different results for the scale factor which should not happen in similar figures. Since we only need two sides to determine the scale factor, let's assume the correct proportion for similar triangles using sides VU to CD and UT to DE, which are the more likely corresponding sides because they match the orientations of the triangles:VU (UV) / CD = 9.6 / 10 = 0.96UT / DE = 12 / 12 = 1In this case, using sides UT and DE, we receive a scale factor of 1, which is contradictory to the notion of a scale factor that's supposed to reduce or enlarge the figures. Given that similar figures should have the same scale factor for all corresponding sides, there seems to be an inconsistency in the given side lengths.Based on these calculations and the apparent inconsistency, there might be an error in the values provided or in the assumption of which sides correspond. If we disregard the irregularity and presume the intention was for the sides to be proportional, then the scale factor based on side UV to CD is 0.96. However, it's important to consult with an instructor or the source of the problem to clarify the correct corresponding sides and values to determine the intended scale factor.
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