Your team is to design a rectangular playground that has 2,160 yd^2 of space.

Question

Your team is to design a rectangular playground that has 2,160 yd^2 of space. Examine different options for the length and width of the playground if one piece of equipment requires at least 15 yd of length. Consider only whole number options. Give three practical options for the dimensions of the playground and explain why you selected each of these options. Of all possible rectangular designs, which design requires the least amount of fencing? Consider only whole number options.

 Can You Please Work It Out So I Can Have A Better Understanding

Answer 1

The general solution to this problem would be starting with prime factoring of the given area:
2160= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

From the list of prime factors we can find many combinations, which satisfy the condition: "at least 15":

15 x 144 = 2160
16 x 135 = 2160
18 x 120 = 2160
20 x 108 = 2160
24 x 90 = 2160
27 x 80 = 2160
30 x 72 = 2160
36 x 60 = 2160
45 x 48 = 2160