Question

Frank wants to fence off a rectangular area that is 40 ft² inches size for a vegetable garden. He is considering three garden lengths of 8ft, 10ft, and 20 feet. He wants to determine which garden would require the least amount of fencing.

Answer 1

The garden with the smallest perimeter, and therefore requiring the least amount of fencing, is the one measuring 8 feet in length, resulting in a perimeter of 26 feet.

Step-by-step explanation:

Choosing the Garden Size for Minimum Fencing

To determine which of the three garden lengths would require the least amount of fencing, we need to calculate the perimeter of each potential rectangle using the given area of 40 ft². For each length option, we will:

1. Divide the area by the length to find the width.
2. Double the sum of the length and width to get the perimeter.

The smallest perimeter will require the least amount of fencing.

Calculations

• 8 ft Length: Width = 40 ft² / 8 ft = 5 ft; Perimeter = 2(8 ft + 5 ft) = 26 ft
• 10 ft Length: Width = 40 ft² / 10 ft = 4 ft; Perimeter = 2(10 ft + 4 ft) = 28 ft
• 20 ft Length: Width = 40 ft² / 20 ft = 2 ft; Perimeter = 2(20 ft + 2 ft) = 44 ft

Therefore, a garden with a length of 8 feet will require the least amount of fencing with a minimum perimeter of 26 feet.