# The ABC triangle is similar to the A1B1C1 triangle. Their areas are 18 cm2 and 288 cm2, respectively. AB = 9cm

**The ABC triangle is similar to the A1B1C1 triangle. Their areas are 18 cm2 and 288 cm2, respectively. AB = 9cm, find the side of the triangle A1B1C1 similar to it**

Similar triangles are triangles in which the corresponding angles are equal and the corresponding sides are proportional.

The coefficient of similarity is the number k equal to the ratio of similar sides of similar triangles.

k = A1B1 / AB;

k = B1C1 / BC;

k = A1C1 / AC.

The ratio of the areas of similar triangles is equal to the square of the similarity coefficient:

S1 / S = k ^ 2.

Thus, the coefficient of their similarity is:

k ^ 2 = 288/18 = 16;

k = √16 = 4.

In order to find the A1B1 side, it is necessary to multiply the length of the AB side by the similarity coefficient:

A1B1 = AB * k;

A1B1 = 9 * 4 = 36 cm.

Answer: the length of the A1B1 side is 36 cm.