You are given a square which you are told has a total area of 100 squared centimetres. You are also told that one side of the square has dimension 4(3x + 2), and the other has dimension 8x - y. What are the values of x and y?

The first thing to know is that a square has equal sides, and that the area of a square is length x length.

Therefore in this case

Length x length = 100    or    Length² = 100

ans so Length = square root of 100 = 10

Now we can say that 4(3x - 2) = 10

Multiply out the brackets  12x - 8 = 10

Add 8 to both sides   12x = 18

Divide both sides by 12     x = 18/12 = (18/6)/(12/6) = 3/2 = 1.5

Now we can substitute in this value for x into our other expession for the length.

8x - y = 10

8(1.5) - y = 10

12 - y = 10

Add y to both sides 12 = 10 + y

Subtract 10 from each side 2 = y

So we have x = 1.5 and y = 2