Answer:Part 1:
To find the length of the south side of the farm, we can look at the figure provided. The south side is the bottom side of the farm, which is made up of two sections: a section with a length of x - 4 and another section with a length of 3x - 4. To find the total length, we add these two lengths together.
South side length = (x - 4) + (3x - 4)
Simplifying this expression, we combine like terms:
South side length = 4x - 8
Therefore, the length of the south side of the farm is 4x - 8.
Part 2:
To find the length of the west side of the farm, we can again refer to the figure provided. The west side is the left side of the farm, which consists of a single section with a length of 2x + 2.
Therefore, the length of the west side of the farm is 2x + 2.
Part 3:
To find the overall area of the farm, we need to calculate the area of each individual section and then add them together. The area of a rectangle is given by the formula length × width.
Looking at the figure, we can see that the dimensions of each section are:
- The north side has a length of x - 4 and a width of 2.
- The south side has a length of 4x - 8 and a width of 2.
- The east side has a length of 2 and a width of 3x - 4.
- The west side has a length of 2x + 2 and a width of 3.
To find the area of each section, we multiply the length by the width:
- Area of the north side = (x - 4) × 2
- Area of the south side = (4x - 8) × 2
- Area of the east side = 2 × (3x - 4)
- Area of the west side = (2x + 2) × 3
Finally, to find the overall area of the farm, we add the areas of all the sections together:
Overall area = Area of the north side + Area of the south side + Area of the east side + Area of the west side
Overall area = (x - 4) × 2 + (4x - 8) × 2 + 2 × (3x - 4) + (2x + 2) × 3
Simplifying this expression, we combine like terms:
Overall area = 2x - 8 + 8x - 16 + 6x - 8 + 6x + 6
Overall area = 22x - 26
Therefore, the overall area of the given farm is 22x - 26.