Question

a nature reserve plans create a rectangular enclosure to protect a population of 3,600 rabbits. each rabbit requires 2 square meters (m²) of area to roam freely. the enclosure has a fixed width of 60 meters. what should be the length of the enclosure and what is the total length of fencing required to enclose the area? the length of the enclosure is 90 meters, and the total length of the fencing required is 300 meters. the length of the enclosure is 80 meters, and the total length of the fencing required is 280 meters. the length of the enclosure is 100 meters, and the total length of the fencing required is 320 meters. the length of the enclosure is 120 meters, and the total length of the fencing required is 360 meters

Explanation:

Step1: Calculate the total area needed

The total area \(A\) needed for \(3600\) rabbits, with each rabbit requiring \(2\space m^{2}\), is \(A = 3600\times2=7200\space m^{2}\).

Step2: Find the length of the rectangle

The area of a rectangle is \(A = length\times width\). Given \(width = 60\space m\) and \(A = 7200\space m^{2}\), then \(length=\frac{A}{width}=\frac{7200}{60}=120\space m\).

Step3: Calculate the perimeter of the rectangle (total length of fencing)

The perimeter \(P\) of a rectangle is \(P = 2\times(length + width)\). Substituting \(length = 120\space m\) and \(width = 60\space m\), we get \(P=2\times(120 + 60)=2\times180 = 360\space m\).

Answer:

The length of the enclosure is 120 meters, and the total length of the fencing required is 360 meters.