Question

A rectangle patio is surrounded on three sides by a fence. If the areas of the patio is 45 m sq and the total of fence is 19m what is the length and width of the patio?

Answer 1

LW = 45
L + 2W = 19
L = 19-2W

substituting for L :-
W(19-2W) = 45

-2W^2 + 19W = 45

2W^2 - 19W + 45 = 0 
W = 5 or 4.5

If W = 5, L = 9
If W = 4.5, L = 10

So there are 2 possible answers.