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Two Similar Triangles Have A Scale Factor Of 1:3. If The Perimeter Of The Smaller Triangle Is 27, What Is The Perimeter Of The Larger?

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Jeffrey Campbell Profile
Well, there are two ways to solve this problem. One would be to draw two triangles, and lets say the fist triangle's sides are all 9. By adding them up, the perimeter is 27, which is the same as in the problem. Since the scale factor is 1:3, that means the side lengths are 3 times a big, so multiply each side by 3, and the side lengths of the new triangle are all 27. Add them all together and the perimeter of the larger triangle is 81. The other way to do this is to draw two equilateral, isosceles, or any two triangles with the same angles. Since they have the same angles, their perimeters are directly proportional, so you can just multiply 27*3 to get 81 as your perimeter for the larger triangle. Either way works.

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