The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is `20-(35+35)` metres].

Options

A. ` 129.5, 47`
B. `129.5, 48`
C. `127.7, 49`
D. `189.5, 50`

Explanation

To solve the problem of finding the area and perimeter of the garden, which is rectangular in the middle and semi-circular at the ends, follow these steps:

### Step 1: Determine the dimensions of the rectangle
Given that the total length of the garden is \(20 - (35 + 35)\) metres, we can simplify this:

\[ 20 - (35 + 35) = 20 - 70 = -50 \text{ metres (which doesn't make sense)} \]

However, based on the context, we can assume the length of the rectangle is \(20\) metres, and the diameter of the semicircles is \(7\) metres. Therefore, the radius \(r\) of the semicircles is:

\[ r = \frac{7}{2} = 3.5 \text{ metres} \]

The length of the rectangle can be calculated as follows:

\[ \text{Length of rectangle} = 20 - \text{Diameter of semicircles} \]
\[ \text{Length of rectangle} = 20 - 7 = 13 \text{ metres} \]

### Step 2: Calculate the area of the garden
The area of the garden consists of the area of the rectangle and the area of the two semicircles.

1. **Area of the rectangle**:
\[ \text{Area of rectangle} = \text{Length} \times \text{Breadth} = 13 \times 7 = 91 \text{ square metres} \]

2. **Area of the semicircles**:
The area of one semicircle is given by the formula:
\[ \text{Area of semicircle} = \frac{1}{2} \pi r^2 \]
Therefore, the area of two semicircles is:
\[ \text{Area of two semicircles} = 2 \times \frac{1}{2} \pi r^2 = \pi r^2 \]
Substituting \(r = 3.5\):
\[ \text{Area of two semicircles} = \pi \left(\frac{7}{2}\right)^2 = \pi \times \frac{49}{4} = \frac{49\pi}{4} \]
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of two semicircles} = \frac{49 \times 22}{4 \times 7} = \frac{1078}{28} = 38.5 \text{ square metres} \]

3. **Total area of the garden**:
\[ \text{Total Area} = \text{Area of rectangle} + \text{Area of two semicircles} \]
\[ \text{Total Area} = 91 + 38.5 = 129.5 \text{ square metres} \]

### Step 3: Calculate the perimeter of the garden
The perimeter consists of the lengths of the two semicircles and the two lengths of the rectangle.

1. **Perimeter of the semicircles**:
The perimeter of one semicircle is:
\[ \text{Perimeter of semicircle} = \pi r \]
Therefore, the perimeter of two semicircles is:
\[ \text{Perimeter of two semicircles} = 2 \times \frac{1}{2} \pi d = \pi d \]
where \(d = 7\):
\[ \text{Perimeter of two semicircles} = \pi \times 7 \]
Substituting \(\pi \approx \frac{22}{7}\):
\[ \text{Perimeter of two semicircles} = 7 \times \frac{22}{7} = 22 \text{ metres} \]

2. **Perimeter of the rectangle**:
The perimeter of the rectangle is:
\[ \text{Perimeter of rectangle} = 2 \times \text{Length} = 2 \times 13 = 26 \text{ metres} \]

3. **Total perimeter of the garden**:
\[ \text{Total Perimeter} = \text{Perimeter of two semicircles} + \text{Perimeter of rectangle} \]
\[ \text{Total Perimeter} = 22 + 26 = 48 \text{ metres} \]

### Final Answers:
- **Area of the garden**: \(129.5 \text{ square metres}\)
- **Perimeter of the garden**: \(48 \text{ metres}\)