If each side of a regular pentagon is 1 cm, find the length of its diagonal.

Options

A. A)`root(5)(2-3)/2`
B. B)`-1+sqrt5/2`
C. C)`(1+sqrt5)/2`
D. D)data insufficient

Answer

To find the length of the diagonal of a regular pentagon with each side measuring 1 cm, we can follow these steps:

### Step 1: Understand the formula for the diagonal of a regular pentagon.
The length of the diagonal \( d \) of a regular pentagon can be calculated using the formula:
\[ d = \frac{1 + \sqrt{5}}{2} \times a \]
where \( a \) is the length of one side of the pentagon.

### Step 2: Substitute the value of the side length into the formula.
Given that each side of the pentagon is 1 cm, we substitute \( a = 1 \) cm into the formula:
\[ d = \frac{1 + \sqrt{5}}{2} \times 1 \]

### Step 3: Simplify the expression.
This simplifies to:
\[ d = \frac{1 + \sqrt{5}}{2} \text{ cm} \]

### Step 4: Finalize the answer.
Thus, the length of the diagonal of the regular pentagon is:
\[ d = \frac{1 + \sqrt{5}}{2} \text{ cm} \]