A gardener wants to create a rectangular vegetable garden in a backyard. She wants 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)
Let's assume the width of the vegetable garden is x feet.
According to the given information, the length of the garden should be 3 feet longer than its width, so the length is (x + 3) feet.
The area of the garden is given as 180 square feet, so we can write the equation:
Area = length * width
180 = (x + 3) * x
Now we can solve this quadratic equation:
180 = x^2 + 3x
x^2 + 3x - 180 = 0
Factoring or using the quadratic formula, we find that x = 12 and x = -15.
Since the width cannot be negative, we discard the negative solution and conclude that the width of the vegetable garden should be 12 feet.
The length can be found by adding 3 to the width: length = 12 + 3 = 15 feet.
Therefore, the gardener should use the dimensions 12 feet by 15 feet for the vegetable garden.