Height of a electrical pole 14 m and its shade is of 10 m, If all the conditions remain same, then what is the length of a tree whose shade is of 10 m ?

Options

A. 21 m
B. 14 m
C. 30 m
D. 20 m

Answer

To solve the problem, we need to relate the height of the electrical pole to the height of the tree using the lengths of their shadows. Here's a step-by-step solution:

### Step 1: Understand the relationship between height and shadow
The height of an object and the length of its shadow are proportional when the angle of elevation of the sun remains the same. This means we can set up a ratio.

### Step 2: Set up the ratio for the electrical pole
Given:
- Height of the electrical pole (H_p) = 14 m
- Length of the shadow of the electrical pole (S_p) = 10 m

The ratio of height to shadow length for the electrical pole is:
\[ \frac{H_p}{S_p} = \frac{14}{10} \]

### Step 3: Set up the ratio for the tree
Let the height of the tree be \( H_t \) and the length of its shadow (S_t) is also given as 10 m. Thus, we can write the ratio for the tree as:
\[ \frac{H_t}{S_t} = \frac{H_t}{10} \]

### Step 4: Set the two ratios equal
Since the conditions remain the same, we can equate the two ratios:
\[ \frac{H_p}{S_p} = \frac{H_t}{S_t} \]
Substituting the known values:
\[ \frac{14}{10} = \frac{H_t}{10} \]

### Step 5: Solve for the height of the tree
To find \( H_t \), we can cross-multiply:
\[ 14 \times 10 = H_t \times 10 \]
This simplifies to:
\[ H_t = 14 \text{ m} \]

### Conclusion
The height of the tree is 14 meters.