# Find the dimensions of the sides of the triangle ABC, if it is known that AB refers

**Find the dimensions of the sides of the triangle ABC, if it is known that AB refers to BC as 7 to 4, BC refers to AC as 6 to 5, and its perimeter is 64.5.**

1. To find each of the unknown sides of a triangle, consider the formula for the perimeter P.

P = AB + BC + AC.

2. From the known relations, we express the values of AB and AC through the side BC

AB: BC = 7: 4; means AB = BC: 7 * 4 = 7/4 BC.

BC: AC = 6: 5; means AC = BC: 6 * 5 = 5/6 BC.

3. Let’s compose the equation, if by the condition of the problem the perimeter is equal to 64.5.

7/4 BC + BC + 5/6 BC = 64.5;

(21 + 12 + 10) / 12 ВС = 64.5;

43/12 BC = 64.5;

BC = 64.5: 43 * 12 = 18.

Let’s calculate what the side AB is equal to

AB = BC * 7: 4 = 18 * 7: 4 = 31.5.

Find the side of the speaker

AC = BC * 5: 6 = 15.

Answer: The sides are equal to 18, 15 and 31.5