A 20 m long vertical pole casts a shadow 10 m long.At the same time tower makes shadow 50 m long, the tower is _____ long.

Options

A. 75 m
B. 100 m
C. 105 m
D. 120 m

Answer

To find the length of the tower based on the information given about the vertical pole and its shadow, 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 that is 20 m tall and casts a shadow of 10 m. At the same time, a tower casts a shadow of 50 m. We need to find the height of the tower.

### Step 2: Set Up the Similar Triangles
The pole and its shadow form a right triangle, and the tower and its shadow form another right triangle. Since the angles of elevation from the tip of the shadow to the top of the pole and the tower are the same (because they are cast at the same time), the two triangles are similar.

### Step 3: Write the Proportions
For similar triangles, the ratios of the corresponding sides are equal. Therefore, we can set up the following proportion:

\[ \frac{\text{Height of Pole}}{\text{Length of Pole's Shadow}} = \frac{\text{Height of Tower}}{\text{Length of Tower's Shadow}} \]

Substituting the known values:

\[ \frac{20 \text{ m}}{10 \text{ m}} = \frac{h}{50 \text{ m}} \]

Where \( h \) is the height of the tower.

### Step 4: Solve for the Height of the Tower
Cross-multiply to solve for \( h \):

\[ 20 \times 50 = 10 \times h \]

This simplifies to:

\[ 1000 = 10h \]

Now, divide both sides by 10:

\[ h = \frac{1000}{10} = 100 \text{ m} \]

### Conclusion
The height of the tower is **100 m**.

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