A rectangular chicken yard was built against an existing shed wall. 30 m of fencing was used to enclose 108 m^2. Find the dimensions of the yard.
Let's assume the length of the rectangular chicken yard is L, and the width is W.
We know that the perimeter of a rectangle is given by:
2L + 2W = 30 m
We also know that the area of a rectangle is given by:
L * W = 108 m^2
Now let's solve the system of equations. We can start by isolating L in the first equation:
2L + 2W = 30
2L = 30 - 2W
L = 15 - W
Now substitute this expression for L into the second equation:
(15 - W) * W = 108
15W - W^2 = 108
Rearrange this equation into standard quadratic form:
W^2 - 15W + 108 = 0
Now let's solve this quadratic equation by factoring:
(W - 9)(W - 12) = 0
So, W = 9 or W = 12
If W = 9, then L = 15 - 9 = 6
If W = 12, then L = 15 - 12 = 3
Therefore, the possible dimensions of the rectangular chicken yard are 9 m by 6 m or 12 m by 3 m.