1200 poles were used to put up a fence around the rectangular garden of length y meters and width 80 meters. Given that the poles were planted 400 cm apart, calculate the value of y.

First, we need to calculate the total length of the fence, which is the perimeter of the rectangular garden.

Perimeter = 2(length + width)
Perimeter = 2(y + 80)

Next, we need to calculate the number of poles needed for the length of the fence. Since the poles were planted 400 cm apart, we need to convert the length of the fence from meters to centimeters.

Total length of the fence = Perimeter * 100 (to convert meters to centimeters)

Number of poles for the length = Total length of the fence / 400

Given that 1200 poles were used in total, we can set up the equation:

Number of poles for the length + Number of poles for the width = 1200
Total length of the fence / 400 + 80 / 400 = 1200
(2(y + 80) * 100) / 400 + 80 / 400 = 1200
(2(y + 80) * 100 + 80) / 400 = 1200
(200y + 16000 + 80) / 400 = 1200
(200y + 16080) / 400 = 1200
200y + 16080 = 1200 * 400
200y + 16080 = 480000
200y = 480000 - 16080
200y = 463920
y = 463920 / 200
y = 2319

Therefore, the value of y is 2319 meters.

The total perimeter of the rectangular garden is 2(length + width) meters.

Given that the poles were planted 400 cm apart, we need to convert 400 cm to meters: 400 cm = 400/100 meters = 4 meters.

Therefore, the total number of poles required is equal to the total perimeter divided by the distance between each pole:

1200 = 2(y + 80) / 4

Simplifying the equation:

1200 = (y + 80) / 2

Multiplying both sides by 2:

2400 = y + 80

Subtracting 80 from both sides:

2320 = y

Therefore, the value of y, the length of the rectangular garden, is 2320 meters.