Answer: 30 cm
Reason:
The median of a triangle goes from a vertex to the midpoint of the opposite side.
The median of an equilateral triangle will divide the triangle into two congruent 30-60-90 right triangles.
These special types of triangles have the property that:
long leg = shortLeg*sqrt(3)
The median represents the long leg, as it's opposite the 60 degree angle. The short leg must be 5 cm long to fit the template above.
The short leg doubles to 5*2 = 10 cm which is the length of each side of this equilateral triangle.
See the diagram below.
The equilateral triangle has 3 sides of 10 cm each, therefore the perimeter is 3*10 = 30 cm.