The areas of two similar triangles are 6 and 24. The perimeter of one is greater than

The areas of two similar triangles are 6 and 24. The perimeter of one is greater than the perimeter of the other by 6. Find the perimeter of the larger triangle.

Given:
triangle ABC is similar to triangle A1B1C1,
S ABC = 6 centimeters,
S A1B1C1 = 24 centimeters,
P A1B1C1 – P ABC = 6 centimeters.
Find Р А1В1С1 -?
Solution:
Consider similar triangles ABC and A1B1C1. We know that the ratio of the areas of similar triangles is equal to the square of the similarity coefficient. Then K ^ 2 = S A1B1C1 / S ABC = 24/6 = 4, then K = 2.
Therefore, the perimeter of the larger triangle, that is, P A1B1C1 = 2 * 6 = 12 (centimeters).
Answer: 12 centimeters.