The perimeter of a triangle is 144 cm, and its sides are 9: 11: 16. Find the sides of the triangle.

Since the sides of the triangle are given in the ratio 9: 11: 16 = AB: BC: AC, you can enter the proportionality coefficient k and express the lengths of the sides through it:

AB = 9k;

BC = 11k;

AC = 16k.

Perimeter is the sum of the lengths of all sides of the shape. We get the following equation:

9k + 11k + 16k = 144;

36k = 144;

k = 144/36;

k = 4.

Performing the reverse replacement, we get:

AB = 9 • 4 = 36;

BC = 11 • 4 = 44;

AC = 16 • 4 = 64.

Answer: 36, 44 and 64.