The perimeter of triangle ABC is 22 cm. Find the lengths of the sides of this triangle if AB refers to BC

The perimeter of triangle ABC is 22 cm. Find the lengths of the sides of this triangle if AB refers to BC as 5: 4, and BC refers to AC as 2: 1.

By the condition of the problem, the perimeter P of the triangle ABC is 22 cm:

P = AB + BC + AC = 22.

We also have that:

AB / BC = 5/4,

BC / AC = 2/1.

Then we get that

BC = 2 * AC and AB = 5/4 * BC = 5/4 * 2 * AC = 5/2 * AC.

Consequently,

AB + BC + AC = 22,

5/2 * AC + 2 * AC + AC = 22,

11/2 * AC = 22,

AC = 4.

Let’s substitute the AC value in the expressions obtained above:

AB = 5/2 * AC = 5/2 * 4 = 10,

BC = 2 * AC = 2 * 4 = 8.

So, the sides of triangle ABC:

AB = 10, BC = 8, AC = 4.

Answer: AB = 10, BC = 8, AC = 4.