Acrivity 1 There is a path of $$ I $$ me widh arenand the thack. 1.1 Calculate the circumference of one scmi-circle of the track. 1.2 Caleulate the perimeter of the total track. $$ \mathrm{I} m $$ in width. Caleulate the 1.3 There is a path around the track, w. area of the path. 1.4 The athletics club manager wants to ercet a fence one metre from the track (on the outside perimeter of the path). Calculate how many metres of fencing he will have to buy. 1.5 The fence must be supported by poles planted three metres apart. How many poles are needed? If he pays R115,95 per running metre of fencing, what is the cost of

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Let's break down the problem step by step, extracting the known conditions and calculating each part.

### Known Conditions
- The width of the path around the track is $$ I $$ meters.
- The track is circular, and we will assume it consists of two semicircles and two straight sections (like a standard athletics track).

### Step 1: Calculate the Circumference of One Semicircle of the Track
The circumference $$ C $$ of a full circle is given by the formula:
$$
C = 2\pi r
$$
For a semicircle, the circumference is half of that:
$$
C_{\text{semicircle}} = \pi r
$$
Where $$ r $$ is the radius of the semicircle.

### Step 2: Calculate the Perimeter of the Total Track
The total perimeter $$ P $$ of the track consists of two semicircles and two straight sections. If we denote the length of the straight sections as $$ L $$, the total perimeter can be expressed as:
$$
P = 2 \cdot C_{\text{semicircle}} + 2L
$$

### Step 3: Calculate the Area of the Path
The area $$ A $$ of the path can be calculated by finding the area of the larger rectangle (including the path) and subtracting the area of the smaller rectangle (the track itself).

### Step 4: Calculate the Fencing Requirement
The fencing will be erected 1 meter from the outer edge of the path. Therefore, we need to calculate the new perimeter, which will be the outer perimeter of the path.

### Step 5: Calculate the Number of Poles Needed
The poles are planted 3 meters apart, so we will divide the total length of the fencing by 3 to find the number of poles needed.

### Step 6: Calculate the Cost of the Fencing
The cost can be calculated by multiplying the total length of fencing by the cost per meter.

Now, let's perform the calculations. However, we need the value of $$ I $$ to proceed. Please provide the width $$ I $$ of the path.
To calculate the required measurements and costs for the athletics track and fencing: 1. **Circumference of One Semicircle**: $$ C_{\text{semicircle}} = \pi r $$ (Where $$ r $$ is the radius of the semicircle.) 2. **Perimeter of the Total Track**: $$ P = 2 \cdot C_{\text{semicircle}} + 2L $$ (Where $$ L $$ is the length of the straight sections.) 3. **Area of the Path**: $$ A = \text{Area of larger rectangle} - \text{Area of smaller rectangle} $$ 4. **Fencing Requirement**: - New perimeter = Outer perimeter of the path. - Total fencing needed = New perimeter. 5. **Number of Poles Needed**: $$ \text{Number of poles} = \frac{\text{Total fencing}}{3} \text{ meters apart} $$ 6. **Cost of Fencing**: $$ \text{Cost} = \text{Total fencing} \times R115.95 $$ **Note**: The value of $$ I $$ (width of the path) is required to perform the calculations accurately.

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