Final answer:
To find the length and width of the driveway, one must solve a quadratic equation derived from the area formula and the relation given between length and width. The width can be found using the quadratic formula, and then the length is calculated by applying the relationship between length and width.
Step-by-step explanation:
The question pertains to solving a quadratic equation to find the length and width of a driveway where the width (w) is given in terms of length (l) as l = 8 + 3w and the area of the rectangle is 16 square feet. By setting up the equation lw = 16 and substituting the value of l, we get a quadratic equation in terms of w: (8 + 3w)w = 16. After expanding and rearranging, you will have 3w2 + 8w - 16 = 0, which is a quadratic equation that can be factorized or solved using the quadratic formula.
To factorize, we look for factors of -16 that add up to 8. As there are none, we need to use the quadratic formula, w = (-b ± sqrt(b2 - 4ac))/(2a). By substituting a = 3, b = 8, and c = -16, we can find the potential values for w. We disregard the negative value since width cannot be negative, and we take the positive root, round it to the nearest tenth, and then use it to find the length.
It is important to note that if the width is determined to be w feet, then the length would be 8 + 3w feet.