Answer:
3 feet
Explanation:
You can use the formula for the area of a rectangle:
Area = length x width
You know that the area is 30 ft^2, so we can plug that in:
30 = length x width
You also know that the length is 4 feet longer than twice the width:
length = 2x + 4
Now you can substitute this expression for length into the area formula:
30 = (2x + 4) x width
Simplifying:
30 = 2x^2 + 4x
Dividing both sides by 2:
15 = x^2 + 2x
Rearranging:
0 = x^2 + 2x - 15
Now you can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = 2, and c = -15:
x = (-2 ± sqrt(2^2 - 4(1)(-15))) / (2)(1)
x = (-2 ± sqrt(64)) / 2
x = (-2 ± 8) / 2
x = -5 or x = 3
Since the width of a rectangle can't be negative, the only possible solution is x = 3. Therefore, the width of the rectangle is 3 feet.