Example Question - calculating scale factor
Here are examples of questions we've helped users solve.
Determining Scale Factor in Similar Triangles
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 = 0.96 UT / CE = 12 / 16 = 0.75 As 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 = 0.96 UT / DE = 12 / 12 = 1 In 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.
Finding Scale Factor of Similar Triangles
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 / 9.6 When you divide 12 by 9.6, the result is: Scale factor = 1.25 This 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.
Calculating Scale Factor Between Two Triangles
The image shows two similar triangles with corresponding side lengths given. To find the scale factor, we can divide the length of a side of one triangle by the corresponding side length of the other triangle. From triangle CDE: CD = 10 DE = 12 CE = 5 From triangle VUT: VU = 9.6 UT = 8 VT = ? (we don't know this length, and we don't need it to find the scale factor). Let's use the sides CD and VU for our calculation since both of these corresponding sides are given: VU (from triangle VUT) / CD (from triangle CDE) = 9.6 / 10 = 0.96 Therefore, the scale factor from triangle CDE to triangle VUT is 0.96.
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