Given the diagram for 4 cows, 5 cows, and 6 cows (attached) how many squares of fencing are required for 100 cows?
In order to find the number of squares of fencing needed to fence in 100 cows, I started by looking for what was in common for each fence.
By looking at the diagrams the first thing I notice is that the all three fences have 3 squares on each end, making a total of 6 squares for the ends of each fence.
Therefore, no matter how many cows there are inside the fence, the ends will contain at total of 6 squares.
This leaves the squares that are directly above and below the cows. The number of squares directly above the cows is equal to the number of cows, and the number of squares directly below the cows is equal to the number of cows. This gives you a total of twice the number of cows for the number of squares directly above and below the cows.
If you let n equal the number of cows and s equal the total number of squares needed: `s=2*n+6` .
` 2n` represents the number of squares directly above and below the cows, and ` 6` represents the number of squares on the ends of the fence.
Therefore for ` n=100 ` ; ` ``s=2*100+6=206 ` .
You would need 206 squares of fence to fence in 100 cows.