Find the length and width of a rectangle that has the given area and a minimum perimeter.
Area: 162 square feet?

Question

? · Answer

18 feet (length), 9 feet (width)
Perimeter: 54 feet
Area: 162 feet^2

The Gnostic · Answer

Since the area is 162 feet, the dimensions of the rectangle are a length L and a width 162/L.
The perimeter is P(L) = 2L + 324/L and we want P(L) to be a minimum.
P ' (L) = 2 - 648/L². Set P ' (L) to 0 and:
648/L² = 2
648/2 = L² = 324
L = 18
162/18 =  9
The length is 7feet  and the width is 18 feet.

Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 162 square feet?

2 Answers