The perimeter of the triangle ABC is 51 cm, AB = 18 cm, BC: AC = 5: 6. Prove that angle B = angle C.

The perimeter of a triangle is equal to the sum of the lengths of all its sides. Let’s denote one part by “x”, then the BC side is 5x, and the AC side is 6x. Knowing that the perimeter is 51 centimeters, and the third side is 18 centimeters, we create an equation.

5x + 6x + 18 = 51;

We carry out the addition of similar monomials on the left side of the equation.

11x + 18 = 51;

Move the positive number 18 to the right side of the equation by changing the sign of the number to negative.

11x = 51 – 18;

11x = 33;

x = 33/11;

x = 3.

The BC side is 5 * 3 = 15 cm, and the AC side = 6 * 3 = 18 cm. Since the sides AB and AC are equal, therefore, the angles opposite these sides are also equal.

Answer: 15 cm, 18 cm.