Let's let the width of the rectangle be represented by the variable "w".
We know that the length of the rectangle is 4 feet less than three times the width. So the length can be represented by the expression 3w - 4.
The area of a rectangle is given by the formula A = lw, where A is the area, l is the length, and w is the width. We are given that the area of the rectangle is 55ft^2.
So we can set up an equation:
55 = w(3w - 4)
Expanding the right side of the equation gives:
55 = 3w^2 - 4w
Subtracting 55 from both sides gives:
0 = 3w^2 - 4w - 55
We can solve for w using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 3, b = -4, and c = -55.
Plugging these values into the quadratic formula gives:
w = (4 ± sqrt(16 + 660)) / 6
Simplifying under the square root gives:
w = (4 ± sqrt(676)) / 6
w = (4 ± 26) / 6
So we have two possible values for w:
w = 5.0 or w = -3.6667
Since the width of the rectangle must be a positive value, we can reject the negative value and conclude that the width of the rectangle is 5.0 feet.
To find the length, we can use the expression we earlier derived:
length = 3w - 4
Substituting in w = 5.0 gives:
length = 3(5.0) - 4
length = 11.0
So the dimensions of the rectangle are:
Width = 5.0 feet
Length = 11.0 feet