Question

Find the dimensions of a rectangle of area 121 ft² that has the smallest possible perimeter.

a) 12 ft by 10 ft
b) 11 ft by 11 ft
c) 15 ft by 8 ft
d) 13 ft by 9 ft
e) 20 ft by 6.05 ft

Answer 1

The dimensions of the rectangle with an area of 121 ft² that has the smallest possible perimeter are 11 ft by 11 ft, forming a square.

Step-by-step explanation:

The goal is to find the dimensions of a rectangle with an area of 121 ft² that has the smallest possible perimeter. To have the smallest perimeter, the rectangle must be as close to a square as possible, because a square has the shortest perimeter of all rectangles with a given area. The area of a rectangle is calculated by multiplying its length by its width, and for a square, this would mean that both dimensions are the same.

If we take the square root of the area, which is √121 ft², we find that each side of the square should be 11 ft, because 11 ft × 11 ft = 121 ft². Therefore, the rectangle that would have the smallest perimeter would be one where both dimensions are equal, i.e., a square with sides of 11 ft each. The other options with different lengths and widths all result in larger perimeters and thus are not the optimal solution.