# 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.

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