Question - Finding Scale Factor of Similar Triangles
Solution:
The image contains two similar right-angled triangles, Triangle CDE and Triangle VUW. We are given the lengths of the sides of each triangle, with side CD being 10 units, DE being 12 units, and CE being unknown but corresponding to side VW which is 9.6 units. We are asked to find the scale factor from Triangle CDE to Triangle VUW.The scale factor is the ratio of the lengths of corresponding sides in similar figures. To determine the scale factor between these two triangles, we can take the lengths of any pair of corresponding sides and divide them. Here, we can use DE and UW since those are the only two corresponding sides both of which we know the lengths. Since DE is the longer side in the larger triangle, we will divide the length of DE by the length of UW to get the scale factor.Let's do the calculation:Scale factor = (Length of DE in Triangle CDE) / (Length of UW in Triangle VUW)Scale factor = 12 / 9.6When you divide 12 by 9.6, the result is:Scale factor = 1.25This means that Triangle CDE is 1.25 times larger than Triangle VUW, or in other words, Triangle VUW is 1.25 times smaller than Triangle CDE. The scale factor is 1.25.
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