The areas of two similar polygons are related as 16:49. The perimeter of the larger polygon is 35.
| January 16, 2021 | education
The areas of two similar polygons are related as 16:49. The perimeter of the larger polygon is 35. Find the perimeter of the smaller polygon.
It is known that the ratio of the perimeters or lengths of the sides of similar triangles is equal to the coefficient of similarity, the ratio of the areas of these triangles is equal to the square of the coefficient of similarity. Knowing the area ratio, we find the similarity coefficient:
k ^ 2 = 16/49;
k = √ (16/49) = 4/7.
The perimeter of the smaller triangle can be found by multiplying the perimeter of the larger one by the coefficient of similarity:
P = 35 * 4/7 = 140/7 = 20.
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