Marc has eight rods of length 12 cm. He forms a rectangle with three rods along the length and one rod along the width. We need to find the minimum length and the minimum perimeter of the rectangle.

1. Problem Description

Marc has eight rods of length 12 cm. He forms a rectangle with three rods along the length and one rod along the width. We need to find the minimum length and the minimum perimeter of the rectangle.

2. Solution Steps

(a) Calculate the minimum length of the rectangle.

The length of the rectangle consists of 3 rods. Since the length of each rod is 12 cm, the total length is $3 \times 12 = 36$ cm.

(b) Calculate the minimum perimeter of the rectangle.

The rectangle has a length of 3 rods and a width of 1 rod. The perimeter of a rectangle is given by the formula:

$P = 2(l + w)$, where $l$ is the length and $w$ is the width.

In this case, $l = 3 \times 12 = 36$ cm and $w = 1 \times 12 = 12$ cm.

Therefore, the perimeter is $P = 2(36 + 12) = 2(48) = 96$ cm.

3. Final Answer

(a) The minimum length of the rectangle is 36 cm.

(b) The minimum perimeter of the rectangle is 96 cm.