Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.

Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.

Farhan's Poor Square

Stage: 4 Challenge Level:

Splendid solutions to Farhan's problem came in from Shabbir
Telani, age 13, Jack Hunt School, Peterborough, Prav Idaikkadar,age
13, and Megan Mitchell, age 14, North London Collegiate School
Maths Club, Richard Mason, Madras College, and Rachel Evans, the
Mount School York. This is Shabbir's solution:

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