# 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.

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