The perimeter of a square is at most 22 feet. let n represent the length of one side of the square part a: write and inequality that represents the situation. ( i think it’s n is greater than or equal to 22 , but just making sure ; ) ) part b: of the lengths 2.5 ft , 4.8 ft , 5.2 ft , 5.8 ft , and 6 ft , which could be the side length of the square. write all that apply. explain your answers and show your work.

Part A

P = perimeter of square
P = add up the four sides
P = N+N+N+N
P = 4*N
where N is the side length of the square

The perimeter of the square is at most 22 ft, which means 22 ft is the largest the perimeter can be. Think of it as the ceiling. 

So P = 22 or P < 22. We can combine those two ideas to get  (P is less than or equal to 22)

Replace P with 4N and solve for N


 

divide both sides by 4





The side length N can be 5.5 ft or smaller

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Part B

The result we got from part A above was which means N can be equal to 5.5 or it can be smaller than 5.5

So this describes N = 2.5, N = 4.8, and N = 5.2
The values N = 5.8 and N = 6 are too big

So the answers to part B are 2.5 ft, 4.8 ft, and 5.2 ft

The total would be 40.53