Question

question 13 of 20: you are planning a store on a large lot. your budget only allows for 800 linear feet of walls. what is the maximum squa footage of your store? a) 800 b) 3200 c) 40,000 d) 640,000

Explanation:

Step1: Determine the shape for maximum area

For a given perimeter, a square has the maximum area among rectangles. Let the side length of the square be \(s\). The perimeter of a square \(P = 4s\). Given \(P=800\) feet.

Step2: Solve for the side length

From \(P = 4s\), we can solve for \(s\):

$$s=\frac{P}{4}=\frac{800}{4} = 200$$

Step3: Calculate the area

The area of a square \(A=s^{2}\). Substitute \(s = 200\) into the formula:

$$A=(200)^{2}=40000$$

Answer:

C. 40,000