### 1.1 Define the term perimeter according to the given context.
The perimeter of a shape is the total distance around the outside of that shape. In the context of Sam's vegetable garden, the perimeter is the total length of the fence needed to enclose the garden, including all sides but excluding the width of the gate.
### 1.2 Calculate the perimeter of the garden.
To calculate the perimeter, we sum up the lengths of all sides of the garden and then subtract the width of the gate since the gate space does not need fencing.
The dimensions of the garden are given as follows:
- One side: 8.5 m
- Another side: 2 m
- Another side: 5.5 m
Since it is a rectangular garden, each dimension has an opposite side with the same length. So, the two additional sides will also have lengths of 8.5 m, 2 m, and 5.5 m respectively.
First, calculate the total sum of all side lengths:
[tex]\[ 2 \times (8.5 + 2 + 5.5) \][/tex]
Next, subtract the width of the gate:
[tex]\[ \text{Perimeter } = 2 \times (8.5 + 2 + 5.5) - 1 \][/tex]
Summing the lengths:
[tex]\[ 8.5 + 2 + 5.5 = 16 \][/tex]
Doubling this sum:
[tex]\[ 2 \times 16 = 32 \][/tex]
Subtract the width of the gate:
[tex]\[ 32 - 1 = 31 \][/tex]
Thus, the perimeter of the garden is:
[tex]\[ 31.0 \text{ meters} \][/tex]
### 1.3 Calculate how many panels Sam needs for the fence.
Each fence panel is 1.5 meters wide. To find out how many panels Sam needs, we divide the total perimeter by the width of one panel:
[tex]\[ \text{Panels needed} = \frac{\text{Perimeter}}{\text{Panel width}} \][/tex]
Substitute the values:
[tex]\[ \text{Panels needed} = \frac{31.0}{1.5} \approx 20.666666666666668 \][/tex]
Since Sam can't purchase a fraction of a panel in practice, we need to round up to the next whole number. Therefore, rounding 20.666666666666668 up:
[tex]\[ \text{Panels needed rounded up} = 21 \][/tex]
Summary:
- The perimeter of Sam's garden is 31.0 meters.
- Sam will need 21 panels to fence the entire garden.
