Question

Prove that equilateral ∆ can be constructed on any given line segment .

Answer 1

Let x be the length of the sides of an equilateral triangle.

Now in a triangle, sum of any two sides is always greater than the third side.

In this case, Sum of any two sides = x + x = 2x which is more than x.

Hence the construction of an equilateral triangle on any given line segment is possible.

Above given answer by other expert is also correct but it is by geometry