Here, we have a rectangle with area 24 square meters and we want to determine the largest and smallest perimeter from it.
Mathematically, the area of a rectangle can be calculated using the formula;
A = length * width
Now, we need to know the dimensions of the rectangle that has this area.
Let us take a look at the factors of 24
1, 2 , 3 , 4, 5, 6 , 8 , 12 and 24
So the pairs of values that can give the area 24 square meters include;
1 and 24
2 and 12
3 and 8
4 and 6
Now for each of these pairs, we shall calculate the perimeter
Mathematically, the perimeter P of a rectangle = 2(l + b)
For the first pair
Perimeter will be 2(1 + 24) = 2(50) = 100 meters
For the second pair;
2(2 + 12) = 2(14) = 28 meters
For the third pair;
2(3 + 8) = 2(11) = 22 meters
For the last pair;
2(4 + 6) = 2(10) = 20 meters
So the dimensions giving the smallest perimeter is a rectangle with sides 4 m by 6 m
The dimensions giving the largest perimeter is a rectangle with sides 24 m by 1m