Answer: a. 1 feet by 13 feet
Explanation:
Let L represent the length of the rectangular vegetable garden.
Let W represent the width of the rectangular vegetable garden.
She wants to have a total area of 13 square feet. This means that
LW = 13 - - - - - - - - - - -1
The garden should be 12 feet longer than it is wide. This means that
L = W + 12
Substituting L = W + 12 into equation 1, it becomes
W(W + 12) = 13
W² + 12W = 13
W² + 12W - 13 = 0
W² + 13W - W - 13 = 0
W(W + 13) - 1(W + 13)
W - 1 = 0 or W + 13 = 0
W = 1 or W = - 13
Since the width cannot be negative, then W = 1 feet
L = W + 12 = 1 + 12
L = 13 feet