In an isosceles trapezoid, the side is equal to the midline, and the perimeter is 48 cm to determine the side of the trapezoid.

An isosceles trapezoid is called, in which the sides are equal:

AB = BC.

The perimeter of a trapezoid is the sum of all its sides:

P = AB + BC + СD + AD.

The midline of the trapezoid is the line segment that connects the midpoints of the sides. It is parallel to its bases and equal to their half-sum:

m = (BC + AD) / 2.

BC + AD = 2m.

Since the lateral sides AB and СD are equal to the length of the midline:

AB = СD = m, then:

AB + СD = 2m.

In this way:

AB + СD + BC +AD = 2m + 2m = 4m;

P = 4m;

m = P / 4;

m = 48/4 = 12 cm;

AB = СD = 12 cm.

Answer: the length of the sides of the trapezoid is 12 cm.