If the perimeter of a semi-circle is 144 cm, find its radius (in cm).

Options

A. 56
B. 29
C. 28
D. 58

Answer

To find the radius of a semi-circle given that its perimeter is 144 cm, we can follow these steps:

### Step 1: Understand the formula for the perimeter of a semi-circle.
The perimeter \( P \) of a semi-circle can be calculated using the formula:
\[ P = \pi r + 2r \]
where \( r \) is the radius of the semi-circle.

### Step 2: Set up the equation.
Given that the perimeter \( P \) is 144 cm, we can set up the equation:
\[ \pi r + 2r = 144 \]

### Step 3: Factor out \( r \).
We can factor out \( r \) from the left side of the equation:
\[ r(\pi + 2) = 144 \]

### Step 4: Solve for \( r \).
To find \( r \), we divide both sides of the equation by \( \pi + 2 \):
\[ r = \frac{144}{\pi + 2} \]

### Step 5: Substitute the value of \( \pi \).
Using \( \pi \approx 3.14 \):
\[ r = \frac{144}{3.14 + 2} = \frac{144}{5.14} \]

### Step 6: Calculate the value.
Now, we can calculate \( r \):
\[ r \approx \frac{144}{5.14} \approx 28.03 \]
Rounding this to the nearest whole number, we find:
\[ r \approx 28 \text{ cm} \]

### Final Answer:
The radius of the semi-circle is approximately **28 cm**.

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