suppose you have ABC with AB=5, BC=7, and CA=10, and also EFG with EF=900, FG=1260, and GE=18/00. are these triangles similar, and if so what is the scale factor?
To determine if two triangles are similar, we need to compare the ratios of their corresponding side lengths. In this case, we have triangle ABC and triangle EFG.
First, let's calculate the ratio of the side lengths in triangle ABC:
AB/EF = 5/900
BC/FG = 7/1260
CA/GE = 10/(18/00)
Next, simplify each ratio:
AB/EF = 1/180
BC/FG = 1/180
CA/GE = 10/(1/180) = 1800
Notice that all three ratios are equal to 1/180. Therefore, the triangles are similar.
To find the scale factor, we can take the ratio of any two corresponding side lengths. Let's use AB/EF:
AB/EF = 1/180
The scale factor of the triangles is the reciprocal of this ratio:
Scale Factor = 180/1 = 180
Thus, the scale factor of triangle ABC to triangle EFG is 180.