The perimeter of the ABC triangle is 36 cm. The BC side is 2 1/3 times larger than

| September 2, 2021 | education

The perimeter of the ABC triangle is 36 cm. The BC side is 2 1/3 times larger than the AB side and 2 cm less than the AC side. Find the sides of the triangle.

Let side AB of triangle ABC be x cm, then side BC is 2 1/3 x cm, and side AC is (2 1/3 x + 2) cm (if side BC is 2 cm less than side AC, then side AC, vice versa , 2 cm more than the BC side). By the condition of the problem, it is known that the perimeter of the triangle ABC (the perimeter of the triangle is equal to the sum of its three sides; P = AB + BC + AC) is equal to (x + 2 1/3 x + (2 1/3 x + 2)) cm or 36 cm Let us compose the equation and solve it.

x + 2 1/3 x + (2 1/3 x + 2) = 36;

x + 2 1/3 x + 2 1/3 x + 2 = 36;

5 2/3 x = 36 – 2;

17/3 x = 34;

x = 34: 17/3;

x = 34 * 3/17;

x = 6 (cm) – AB side;

2 1/3 * x = 7/3 * 6 = 14 (cm) – BC side;

2 1/3 x + 2 = 14 + 2 = 16 (cm) – speaker side.

Answer. AB = 6 cm, BC = 14 cm, AC = 16 cm.



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