Question

If Eric Tangler's vegetable garden has an area of 54 square feet and the width is 3 feet less than the length, what is the length of the garden?

a) 9 feet
b) 12 feet
c) 15 feet
d) 18 feet

Answer 1

The length of Eric Tangler's vegetable garden is 9 feet. We calculate this by setting up a quadratic equation based on the area and the given relationship between the length and width, then solving it.

Step-by-step explanation:

The problem involves finding the length of Eric Tangler's rectangular vegetable garden given its area and the relationship between its length and width. The area of the garden is 54 square feet, and the width is 3 feet less than the length. We let x represent the length; therefore, the width becomes x - 3 feet. The area of a rectangle is calculated by multiplying the length by the width, leading to the equation x(x - 3) = 54.

Solving the quadratic equation:

1. Set up the equation based on the area formula: x(x - 3) = 54.
2. Expand and rearrange the equation into standard form: x2 - 3x - 54 = 0.
3. Factor the quadratic equation: (x - 9)(x + 6) = 0.
4. Find possible solutions for x: x = 9 or x = -6.
5. Since a negative length is not possible in this context, the length must be 9 feet.

Therefore, the length of Eric's vegetable garden is 9 feet (Option a).