Find the ratio of the areas of two equilateral triangles if their perimeters are 9 cm and 27 cm.
| May 28, 2021 | education
Let us determine how many times the perimeter of the second triangle is greater than the perimeter of the first, if from the condition of the task we know that the second has 29 centimeters, while the first has 9 centimeters:
27: 9 = 3.
This is the so-called similarity coefficient. After all, triangles are equilateral, which means they are similar.
As we know from the school curriculum, the ratio of the areas of triangles is equal to the square of this coefficient.
Therefore, we determine how many times the area of the second triangle is greater than the area of the first:
32 = 9.
Answer: The area of the second is 9 times the area of the first.
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