Triangles are known to be similar and their areas are 49/64. How do their perimeters relate?
August 30, 2021 | education|
According to the theorem on the areas of similar triangles: the ratio of the areas of similar triangles is equal to the square of the similarity coefficient. That is:
S1 / S2 = k² = 49/64
k = 7/8 is the coefficient of similarity.
According to the theorem on the perimeters of similar triangles: the ratio of the perimeters of such triangles is equal to the coefficient of similarity, that is:
P1 / P2 = k = 7/8.
Answer. P1 / P2 = 7/8.
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