Question

A gardener wants to create a rectangular vegetable garden in a backyard. She wants to have a total area of 13 square feet, and it should be 12 feet longer than it is wide. What dimensions should she use for the vegetable garden?
a. 1 feet by 13 feet
b. 3 feet by 15 feet
c. 6 feet by 9 feet
d. 5 feet by 17 feet​

Answer 1

Answer: a. 1 feet by 13 feet

Step-by-step 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