vertical pole of length 3 m casts a shadow of 7 m and a tower casts a shadow of 28 m at a time. The height of tower is

Options

A. 10 m
B. 12 m
C. 14 m
D. 16 m

Answer

To find the height of the tower based on the given information, we can use the concept of similar triangles. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a vertical pole of height 3 m that casts a shadow of 7 m. A tower casts a shadow of 28 m. We need to find the height of the tower.

### Step 2: Identify the Triangles
Let’s denote:
- The vertical pole as triangle ABC, where:
- AB = height of the pole = 3 m
- BC = length of the shadow of the pole = 7 m
- The tower as triangle DEF, where:
- DE = height of the tower = H (unknown)
- EF = length of the shadow of the tower = 28 m

### Step 3: Set Up the Proportions
Since the two triangles are similar (the angles are the same due to the sun's rays), we can set up the following proportion based on the corresponding sides:

\[ \frac{AB}{DE} = \frac{BC}{EF} \]

### Step 4: Substitute the Known Values
Substituting the known values into the proportion:

\[ \frac{3}{H} = \frac{7}{28} \]

### Step 5: Simplify the Right Side
The fraction \(\frac{7}{28}\) can be simplified:

\[ \frac{7}{28} = \frac{1}{4} \]

So, we have:

\[ \frac{3}{H} = \frac{1}{4} \]

### Step 6: Cross-Multiply to Solve for H
Cross-multiplying gives:

\[ 3 \times 4 = 1 \times H \]

This simplifies to:

\[ 12 = H \]

### Step 7: Conclusion
Thus, the height of the tower (H) is 12 m.

### Final Answer:
The height of the tower is **12 m**.

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