Solve the problem.
-The length of a vegetable garden is 5 feet longer than its width. If the area of the garden is 126 square feet, find its dimensions.
A) w = 10 ft; l = 15 ft
B) w = 8 ft; l = 13 ft
C) w = 9 ft; l = 14 ft
D) w = 8 ft; l = 15 ft

Question

Quizplus · Accepted Answer

Let the width of the garden be w. Then the length of the garden is w+5. The area of the garden is given by A = lw = w(w+5) = 126. Solving for w, we get w=9 or w=-14 (discarding the negative value). Therefore, the width of the garden is 9 feet and the length is 14 feet, which corresponds to choice C. Let's use algebra to solve the problem. Let w be the width of the garden. Then the length of the garden is w + 5 (since it is 5 feet longer than the width). The area of the garden is length times width, or (w+5)w = w^2 + 5w. We are told that this area is 126 square feet, so we can set up the equation:
w^2 + 5w = 126
Rearranging and factoring:
w^2 + 5w - 126 = 0
(w+14)(w-9) = 0
So the possible values for w are -14 and 9, but since w must be a positive measurement, we discard the negative value. Therefore, w = 9, and the length is w+5 = 14. So the dimensions of the garden are 9 feet by 14 feet, which matches answer choice C.

Solve the Problem. -The Length of a Vegetable Garden Is 5 Feet Longer