Answer:
19.25 feet
Explanation:
Let x be the width of the rectangle in feet. Then, the length of the rectangle is x + 3.5 feet. Since the area of a rectangle is equal to its length times its width, we know that the area of the rectangle is (x + 3.5) * x = 65 square feet.
We can solve for x by setting up the equation (x + 3.5) * x = 65 and then solving for x. This gives us the following:
x^2 + 3.5x - 65 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = 3.5, and c = -65, so we have:
x = (-3.5 +/- sqrt(3.5^2 - 4(1)(-65))) / 2(1)
Solving for x, we get:
x = (-3.5 +/- sqrt(12.25 + 260)) / 2
Therefore, the width of the rectangle is x = (-3.5 +/- 19.25) / 2 = -0.75 or 15.75 feet. Since the length of the rectangle is x + 3.5 feet, this means that the length of the rectangle is (-0.75 + 3.5) feet or (15.75 + 3.5) feet, which is equal to 2.75 feet or 19.25 feet.
However, we know that the length of the rectangle must exceed its width by 3.5 feet, so the only solution that is physically possible is x = 15.75 feet and the length of the rectangle is 19.25 feet. Therefore, the length of the rectangle is 19.25 feet.