In triangle ABC, the ratio of AB to BC is 7/4 and the ratio of BC to AC is 6/5. Find all sides of the triangle

In triangle ABC, the ratio of AB to BC is 7/4 and the ratio of BC to AC is 6/5. Find all sides of the triangle if its perimeter is 64.5 cm.

We introduce the coefficient of proportionality k, then the sides of this triangle will be:
AB = 7k;
BC = 4k.
BC / AC = 4k / AC = 6/5;
AC = 20k / 6 = 10k / 3.
By condition, it is known that the perimeter of the triangle is 64.5 cm.We make the equation:
P = AB + BC + AC
7k + 4k + 10k / 3 = 64.5
21k + 12k + 10k = 193.5
43k = 193.5
k = 4.5
Find the sides of the triangle:
AB = 7 * 4.5 = 31.5 (cm);
BC = 4 * 4.5 = 18 (cm);
AC = 10 * 4.5 / 3 = 45/3 = 15 (cm).
Answer: 31.5 cm, 18 cm, 15 cm – the lengths of the sides of the triangle.