The perimeter of a rectangle is 36cm. if the area of the rectangle is 56cm2 find the length and width of the rectangle. let the length be the smaller of the two numbers, and the width the larger.

Are you sure you want the length to be smaller than the width? It's not exactly the way they're defined. I'll solve it that way, but it's an odd question.

Equations
P = 2L + 2W 
Area = L*W

Substitution and Solve
2L + 2W = 36
L*W = 56

Divide the first equation by 2
L + W = 36/2
L + W = 18
Solve for L
L = 18 - W


Put this result in the second equation
W(18 - W) =  56 Remove the brackets
18W - W^2 = 56 Transfer the Left Side to the Right.
0 = W^2 - 18W + 56 Factor
0 = (W - 14)(W - 4)

W - 14 = 0
W = 14 <<<<<Answer
W - 4 = 0
W = 4

Comment
Both 14 and 4 are in cm
W = 14 cm <<<< answer
L = 4 <<<<< answer