how to find perimeter without the area ?

Question

a farmer wants to fence in 3 square garden plots situated along the road and he decides not to install fencing along the edge of the road. if he has 182 ft of fencing material total, what dimensions should he make the square plot?

Answer 1

Nowhere does the problem statement say that the 3 gardens are all the same size. If the farmer is smart, and has made one garden to be large, and the other two small, the farmer will have the most fenced garden area:

Area assuming 3 equal and non-adjacent gardens: 3*(182/9)² = 1227 sq ft (approx)

Area assuming 3 equal and adjacent gardens: 3*(182/7)^{2 =} 2028 sq ft

Area assuming unequal-sized gardens: (182/3)² = 3680 sq ft (approx)

Answer 2

If you visualize this or draw a picture, you would notice that there are 2 ways that this could be possible to create. The first being that the three gardens are not sharing any fences. The other being that that all three gardens are connected. In the first scenario you would have a total of 9 sides since one side on each would not be fenced. The other option is to have them connected and share a fence between them which would mean only having 7 fences. Since you said that the gardens would be squares, you know that all the sides will be of equal length. Therefore, you can just divide the total amount of fencing by the number of sides. You could either have a length of 182/9 = 20.22 ft, or 182/7 = 26 feet depending on which way you set up the gardens. To maximize area, you would assume that you would use the larger length.

Answer 3

Draw and label a diagram!!!

Four lengths of fence are perpendicular to the road.

Represent each length by w. That is 4w.

Three lengths of fence are perpendicular to these three to complete the squares.

That is 3w.

So 3w + 4w = 182

Can you solve for w and answer?