A girl 1.2 metre tall casts a shadow 1.1 m at the time when a building casts a shadow 6.6 m long. The height of the building is

Options

A. 2.7 m
B. 7.2 m
C. 6.0 m
D. 5.5 m

Answer

To find the height of the building based on the shadow lengths of the girl and the building, we can use the concept of similar triangles. The ratio of the height of the girl to the length of her shadow will be equal to the ratio of the height of the building to the length of its shadow.

### Step-by-step Solution:

1. **Identify the given information**:
- Height of the girl (H_g) = 1.2 meters
- Length of the girl's shadow (S_g) = 1.1 meters
- Length of the building's shadow (S_b) = 6.6 meters
- Height of the building (H_b) = ?

2. **Set up the proportion**:
We can set up the proportion based on the heights and shadows:
\[ \frac{H_g}{S_g} = \frac{H_b}{S_b} \]
Substituting the known values:
\[ \frac{1.2}{1.1} = \frac{H_b}{6.6} \]

3. **Cross-multiply to solve for H_b**:
Cross-multiplying gives us:
\[ 1.2 \times 6.6 = 1.1 \times H_b \]
This simplifies to:
\[ 7.92 = 1.1 \times H_b \]

4. **Solve for H_b**:
To find H_b, divide both sides by 1.1:
\[ H_b = \frac{7.92}{1.1} \]

5. **Calculate the value**:
Performing the division:
\[ H_b = 7.2 \text{ meters} \]

### Final Answer:
The height of the building is **7.2 meters**.