the diagram shows a square (6x - 1) cm by (4x + 6) cm find the length of the side of the square

Since the diagram is a square and squares have equal sides, you set the the equations equal to each other because they'd have the same measurement. 

6x - 1 = 4x + 6

Subtract 4x from each side.

2x - 1 = 6

Add 1 to each side. 

2x = 7

Divide by 2 to isolate the variable. 

x = 7/2

Now plug this in to either equation to find the length of the side. 

6(7/2) - 1 = 21 - 1 = 19 cm.