A quadrilateral has a perimeter of 42cm. Three sides have equal length and the fourth side is longer by 6cm. What is the length of the fourth side?

We can call the sides of the equal lengths "x".
We can then make an equation to satisfy the relationship between the perimeter and the length of the sides as follows:
x + x + x + (x + 6) = 42
Therefore 4x + 6 = 42
Now subtract 6 from both sides:
4x = 36, so x = 9.
The length of the fourth side is (x + 6) so:
9 + 6 = 15cm