If we take a square, the area can be as big as 63. However, in case of the thinnest rectangle, the area can be really small as well. So i picked D. But the answer key says A.
what would the amount of fencing be for that thin rectangle?
okay but can we find cases where fencing amount is smaller than 60?
I am not that good at explaining but I will try my best, so the area is 250 square meters and it is constant so you gotta assume, what if it were a square? Becuz if you keep thinking of it as rectangle you will have L x B = 250 and 2 x (L + B) which pretty much leaves you no where.
So assuming its a square L x L = 250
L = 5 x root of 10
L = 15.811 m
so perimeter of square will be 63.25 m which is bigger than 60 meters.
The thing is they have just asked for the perimeter not length and breadth of rectangular plot so you gotta imagine it like what if I reduce the length and increase the breadth by the same number that will give you the same area and the same perimeter.
Hope you understood
that’s a question you can answer through experimentation
okay but could we have cases where perimeter is <=60?
The only cases where the perimeter can be less than 60 is if the number of sides are reduced and the only cases where the perimeter (or area) can increase 63.25 is if the number of sides are increased. That is why circle is the perfect shape for occupying maximum area because it has infinite sides