A gardener wants to create a rectangular vegetable garden in a backyard. She wants it to have a total area of 180 square feet, and it should be 3 feet longer than it is wide. What dimensions should she use for the vegetable garden? (Area = length * width)(1 point)
Responses
12 feet by 15 feet
12 feet by 15 feet
3 feet by 60 feet
3 feet by 60 feet
3 feet by 180 feet
3 feet by 180 feet
15 feet by 18 feet
To find the dimensions of the rectangular vegetable garden, we need to solve the equation:
length * width = 180.
We also know that the length is 3 feet longer than the width, so
length = width + 3.
Substituting the second equation into the first equation, we get:
(width + 3) * width = 180.
Expanding the equation, we get:
width^2 + 3width = 180.
Rearranging the equation to a quadratic form, we get:
width^2 + 3width - 180 = 0.
We can factor this equation as:
(width + 15)(width - 12) = 0.
This gives us two possible solutions:
width + 15 = 0 or width - 12 = 0.
Solving for width, we get:
width = -15 or width = 12.
Since a negative width doesn't make sense in this context, we can ignore the first solution.
Therefore, the width of the vegetable garden is 12 feet.
Substituting this value back into the second equation, we find the length:
length = width + 3 = 12 + 3 = 15 feet.
Therefore, the correct dimensions for the vegetable garden are 12 feet by 15 feet.