The shade of 18 ft high pole is 20 ft. Find out the length of shade of 27 ft long pole

Options

A. 36 ft
B. 30 ft
C. 34 ft
D. 40 ft

Explanation

To solve the problem of finding the length of the shade of a 27 ft long pole, we can use the concept of proportionality based on the given information about the 18 ft pole and its shade.

### Step-by-Step Solution:

1. **Identify the given values:**
- Height of the first pole (h1) = 18 ft
- Length of the shade of the first pole (s1) = 20 ft
- Height of the second pole (h2) = 27 ft
- Length of the shade of the second pole (s2) = ?

2. **Set up the proportion:**
Since the lengths of the shades are proportional to the heights of the poles, we can set up the following proportion:
\[ \frac{s1}{h1} = \frac{s2}{h2} \]
Substituting the known values:
\[ \frac{20}{18} = \frac{s2}{27} \]

3. **Cross-multiply to solve for s2:**
\[ 20 \times 27 = 18 \times s2 \]
\[ 540 = 18 \times s2 \]

4. **Divide both sides by 18 to isolate s2:**
\[ s2 = \frac{540}{18} \]
\[ s2 = 30 \]

5. **Conclusion:**
The length of the shade of the 27 ft long pole is **30 ft**.