Farmer Giles has 36 sections of portable fence which are used to make pens for the sheep. Each of these sections is 1 metre long. Each night he arranges the sections into a rectangle. Sometimes he makes it long and narrow and sometimes he makes it more like a square.
How many different rectangles is he able to make?
What is the area of each of these rectangles?
Perimeter = 36 metres
L(ength) + W(idth) = 18 metres
nevermind... solved it already
To find the number of different rectangles Farmer Giles can make with the portable fence sections, we can start by finding all the possible combinations that add up to 18 meters. Since the length and width can be interchanged, we only need to consider combinations where the length is less than or equal to the width.
Let's check each possible combination:
1. If the length is 1 meter, then the width would be 17 meters. This gives us one rectangle with dimensions 1m x 17m.
2. If the length is 2 meters, then the width would be 16 meters. This gives us one rectangle with dimensions 2m x 16m.
3. If the length is 3 meters, then the width would be 15 meters. This gives us one rectangle with dimensions 3m x 15m.
Continuing this process, we find the following combinations:
1m x 17m, 2m x 16m, 3m x 15m, 4m x 14m, 5m x 13m, 6m x 12m, 7m x 11m, 8m x 10m, and 9m x 9m.
So, Farmer Giles can make a total of 9 different rectangles.
Now, to find the area of each rectangle, we simply multiply the length by the width for each combination found above:
Area = Length x Width
1m x 17m = 17 square meters
2m x 16m = 32 square meters
3m x 15m = 45 square meters
4m x 14m = 56 square meters
5m x 13m = 65 square meters
6m x 12m = 72 square meters
7m x 11m = 77 square meters
8m x 10m = 80 square meters
9m x 9m = 81 square meters
So, the areas of the rectangles range from 17 square meters to 81 square meters.