The length of the shadow of a `3m` high pole at a certain time the day is `3.6 m` .What is the height of another pole whose shadow at that time is `54 m` long?

Options

A. `35 m`
B. `37 m`
C. `45 m`
D. none of these

Answer

To solve the problem step by step using the unitary method, follow these steps:

### Step 1: Understand the relationship
We know that the height of the first pole is 3 meters and the length of its shadow is 3.6 meters. We need to find the height of another pole whose shadow is 54 meters long.

### Step 2: Set up the proportion
Using the information from the first pole, we can set up a proportion:
- Height of the first pole (3 m) corresponds to the length of its shadow (3.6 m).

This can be expressed as:
\[ \frac{\text{Height of first pole}}{\text{Length of first shadow}} = \frac{\text{Height of second pole}}{\text{Length of second shadow}} \]
Substituting the known values:
\[ \frac{3 \text{ m}}{3.6 \text{ m}} = \frac{h}{54 \text{ m}} \]
where \( h \) is the height of the second pole.

### Step 3: Cross-multiply to solve for \( h \)
Cross-multiplying gives us:
\[ 3 \text{ m} \times 54 \text{ m} = 3.6 \text{ m} \times h \]
This simplifies to:
\[ 162 = 3.6h \]

### Step 4: Solve for \( h \)
Now, divide both sides by 3.6 to find \( h \):
\[ h = \frac{162}{3.6} \]

### Step 5: Calculate \( h \)
Calculating the division:
\[ h = 45 \text{ m} \]

### Conclusion
The height of the second pole is 45 meters.

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