The length of a rectangle is 4 cm greater than its width. the perimeter is 32 cm. find the length of the rectangle.

Classic Algebra/Geometry question, gotta love it.

[1] Let's first remember how to calculate perimeter of rectangles. We just add up all the sides: two lengths and two widths. P = 2*L + 2*W.

[2] Now to add Algebra to make everyone oh so happy.

Let's give the width a name, say, W (because we are SO creative). The name of the length will be L (again because we are SO creative). The length of the rectangular is 4 cm greater than the width. In symbols, we are saying

L = W + 4

We know the perimeter is 32 cm. So, P = 32.

But, wait a second, didn't I just say that P = 2*L + 2*W before? I did, that's a clue! Since P = 32, it must mean that 32 = 2*L + 2*W.

But, wait, didn't I just say that L = W + 4? I did, that's another clue! That must mean that 32 = 2*L + 2*W is the same thing as

32 = 2 * (W+4) + 2*W [watch out for those parentheses!]

32 = 2*W + 8 + 2*W

32 = 4*W + 8

24 = 4*W

6 = W

So the width is 6 cm. We want the length, which is just L = W + 4 = 6 + 4 = 10. So the length is 10 cm. We are done!