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A street lamp is fixed 6 m above a road. Rohit, who is 1.5 m tall, stands under it so that the tip of his shadow falls 16 m from the foot of the lamp post. How long is his shadow?

Class 10Triangles (Similarity)Geometry — Similarity
  • A12 m
  • B4 m
  • C6 m
  • D10 m

Step-by-Step Solution

The lamp, Rohit and the shadow tip form two similar right triangles that share the angle at the tip, so , i.e. , giving m. 12 m is the distance from the lamp post to Rohit’ feet (16 − 4), not the shadow; 6 m copies the lamp height; 10 m is 16 − 6.
Answer: B) 4 m

Key idea: Similarity vs congruence

**Congruent**: same shape AND same size. All corresponding parts equal.
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).

If two triangles are similar with scale factor :
- Corresponding sides differ by factor .
- Corresponding angles are equal (always, by definition).
- Areas differ by factor — critical fact, and a common test question.

**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).

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