The sides of the triangle are 8 cm, 10 cm, 16 cm. Find the lengths of the sides of a triangle like this one by a factor of 1.5.

To find a triangle like this one, let’s answer the question which triangles are called similar.

Similar triangles are triangles in which:

the corresponding angles are equal;
the corresponding sides are more (less) k times;
k is the coefficient of similarity.
Triangle ABC is similar to triangle A1B1C1 if:

angle A = angle A1, angle B = angle B1, angle C = angle C1.
AB: A1B1 = BC: B1C1 = AC: A1C1 = k.
The connection between the parties AB = A1B1 * k.
to find the sides of a triangle, for k = 1.5, you need to multiply each side of the known triangle by 1.5.

8 * 1.5 = 12

10 * 1.5 = 15

16 * 1.5 = 24

or the triangle could be reduced by 1.5 times, then the sides will be:

8: 1.5 = 16/3 = 5 + 1/3

10: 1.5 = 20/3 = 6 + 2/3

16: 1.5 = 32/3 = 10 + 2/3.

Answer: 12, 15, 24 or 5 + 1/3, 6 + 2/3, 10 + 2/3.