Pale has a piece of string. He ties the ends together and then tries making the loop into different shapes.
He notices that when he makes an equilateral triangle the length of each side is 2 centimetres longer than when he makes a square.
How long is the piece of string?
Solution:
The length of each side of the square will be a quarter of the total length of the string.
The length of each side of the equilateral triangle will be a third of the total length of the string.
We know that the difference in length between 1/4 of the string and 1/3 of the string is 2 centimetres.
The difference between 1/3 (4/12) and 1/4 (3/12) is 1/12.
Therefore 1/12 of the string is 2 centimetres long, and the whole string must be 24 centimetres long.