The perimeter of the triangle is 27 cm. What is the length of the sides of the triangle

The perimeter of the triangle is 27 cm. What is the length of the sides of the triangle, if its second side is 2 cm longer than the first, and the third side is 4 cm shorter than the second.

1. Let’s denote the triangle ABC given in the problem. Let’s write the expression for the perimeter of the triangle ABC:

P = AB + BC + CA.

Let’s designate the length of the first side AB as “X”. Then BC will be “X + 2”. Let us express the CA:

CA = BC – 4 = (X + 2) – 4 = X + 2 – 4 = X – 2.

The perimeter of the triangle is 27 cm. Let’s compose and solve the equation:

27 = X + (X + 2) + (X – 2);

X + X + 2 + X – 2 = 27;

3X = 27;

X = 27/3;

X = 9 (cm) is the length of the AB side.

2. Find the value of the lengths of the sides BC and CA:

BC = 9 + 2 = 11 (cm);

CA = 9 – 2 = 7 (cm).

Answer: the length of the sides of the triangle is 9 cm, 11 cm and 7 cm.