In the figure a semi-circular garden is shown, whose perimeter is 72 m .

To find the dimensions of a semi-circular garden with a given perimeter, we need to understand the components of the perimeter of a semi-circle. The perimeter \( P \) of a semi-circle consists of two parts: 1. The curved part (which is half the circumference of a full circle). 2. The straight part (the diameter of the circle). The formula for the circumference \( C \) of a full circle is given by: \[ C = 2\pi r \] where \( r \) is the radius of the circle. Therefore, the curved part of the semi-circle is: \[ \text{Curved part} = \frac{1}{2} C = \frac{1}{2} \times 2\pi r = \pi r \] The diameter \( d \) of the circle is: \[ d = 2r \] Thus, the total perimeter \( P \) of the semi-circle is: \[ P = \text{Curved part} + \text{Diameter} = \pi r + 2r \] Given that the perimeter \( P \) is 72 m, we can set up the equation: \[ \pi r + 2r = 72 \] Now, we can factor out \( r \): \[ r(\pi + 2) = 72 \] To find \( r \), we can solve for \( r \): \[ r = \frac{72}{\pi + 2} \] Now, we can calculate the value of \( r \) using \( \pi \approx 3.14 \): \[ r \approx \frac{72}{3.14 + 2} = \frac{72}{5.14} \approx 14.0 \text{ m} \] Now, we can find the diameter: \[ d = 2r \approx 2 \times 14.0 \approx 28.0 \text{ m} \] So, the radius of the semi-circular garden is approximately 14.0 m, and the diameter is approximately 28.0 m.