# The perimeter of the triangle ABC is 64 cm, the AB line is 7 cm less

The perimeter of the triangle ABC is 64 cm, the AB line is 7 cm less than the AC side, but 12 cm larger than the BC side. Find the length of each side.

The perimeter of a triangle is the sum of the lengths of all its sides. Let’s write expressions for the sides:

AB = AC – 7 or

AC = AB + 7,

BC = AB – 12.

Let’s sum up all the sides of the triangle, expressed in terms of AB:

AB + AB + 7 + AB – 12 = 64.

Let us simplify this equation as well:

3 * AB – 5 = 64;

3 * AB = 64 + 5;

3 * AB = 69;

AB = 23 cm.

Let’s find the rest of the sides:

AC = AB + 7 = 23 + 7 = 30 cm,

BC = AB – 12 = 11 cm.

Answer: AB = 23 cm, AC = 30 cm, BC = 11 cm.

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