Final answer:
To find the most economical dimensions for fencing a rectangular area with varying fencing costs, we determined that minimizing the length of the side with the higher cost is key. Among the given options, 10 ft x 80 ft would be the most cost-effective choice as it minimizes the length of the side that costs $18 per foot.
correct option is d) 10 ft x 80 ft
Step-by-step explanation:
The question asks for the most economical dimensions to enclose a rectangular area of 800 square feet with different fencing costs on different sides. To minimize costs, we want to minimize the perimeter with the side that has the higher fencing cost.
We can start by expressing the area (A) in terms of length (L) and width (W) as: A = L x W. Given that A is 800 square feet, the relationship becomes 800 = L x W. Next, we have to consider the cost per foot on different sides. Three sides cost $6 per foot, and one side costs $18 per foot. The total cost (C) then is C = 3(W x $6) + L x $18.
To find the most economical dimensions, we want to minimize the total cost. Since minimizing the side with higher cost to the least possible value will lead to a lower overall cost, the rectangular configuration with the smallest length (which costs $18 per foot) would be the most economical. Thus, maximizing width while keeping the area constant will lead to the most economical solution.
Examining the options given: a) 20 ft x 40 ft, b) 30 ft x 30 ft, c) 40 ft x 20 ft, d) 10 ft x 80 ft, the most economical would be d) 10 ft x 80 ft, since the expensive side is the shortest possible.