At a particular time of a day a 7-m high flagstaff casts a shadow which is 8.2 m long.What is the height of the building which casts a shadow 20.5 metres length at the same moment?

Answer

To find the height of the building that casts a shadow of 20.5 meters when a 7-meter high flagstaff casts a shadow of 8.2 meters, we can use the concept of the unitary method. Here’s a step-by-step solution:

### Step 1: Understand the relationship between height and shadow
The height of the flagstaff and the length of its shadow are proportional. This means that if we know the height of the flagstaff and the length of its shadow, we can find the height of the building using the length of its shadow.

### Step 2: Set up the proportion
Let:
- Height of the flagstaff = 7 meters
- Length of the flagstaff's shadow = 8.2 meters
- Height of the building = \( h \) meters
- Length of the building's shadow = 20.5 meters

We can set up the proportion as follows:
\[ \frac{\text{Height of flagstaff}}{\text{Length of flagstaff's shadow}} = \frac{\text{Height of building}}{\text{Length of building's shadow}} \]
This translates to:
\[ \frac{7}{8.2} = \frac{h}{20.5} \]

### Step 3: Cross-multiply to solve for \( h \)
Cross-multiplying gives us:
\[ 7 \times 20.5 = h \times 8.2 \]
Calculating the left side:
\[ 7 \times 20.5 = 143.5 \]
So we have:
\[ 143.5 = h \times 8.2 \]

### Step 4: Solve for \( h \)
To find \( h \), divide both sides by 8.2:
\[ h = \frac{143.5}{8.2} \]
Calculating this gives:
\[ h \approx 17.5 \text{ meters} \]

### Final Answer
The height of the building is approximately **17.5 meters**.

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