The area ratio of two similar triangles is 9: 1. The sides of the first are 12m, 21m, 27m. Find the sides of the 2nd triangle.

1. Let’s denote the coefficient of similarity through k.

2. As you know, the ratio of the areas of similar triangles is equal to the square of the similarity coefficient, that is

k ^ 2 = 9;

k = 3 or -3.

-3 – does not meet the condition of the problem.

3. What is the first side of the second triangle?

12: 3 = 4 (cm).

4. How long is the second side of the second triangle?

21: 3 = 7 (cm).

5. What is the third side of the second triangle?

27: 3 = 9 (cm).

Answer: the sides of the second triangle are 4 cm, 7 cm and 9 cm.