The angles FDE and DEF of the triangle DEF are equal. The base of the triangle is 2cm longer than the other sides.

The angles FDE and DEF of the triangle DEF are equal. The base of the triangle is 2cm longer than the other sides. The perimeter of a triangle is 14.6 cm. Equate and calculate the lengths of the sides of the triangle.

1. Since the angles FDE and DEF of triangle DEF are equal, then triangle DEF is isosceles with base DE. Let’s designate the length of the hip of the triangle “X” (DF = FE = X), then the base of DE will be “X + 2”.

Let’s compose and solve the equation:

P = DF + FE + DE;

14.6 = X + X + (X + 2);

3X = 12.6;

X = 4.2 (cm) is the length of the thigh.

2. Find the base:

4.2 + 2 = 6.2 (cm.)

Answer: The lengths of the sides of the triangle DEF are 4.2 cm, 4.2 cm and 6.2 cm.