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At the same moment on a sunny morning, a vertical rod 1.2 m tall casts a shadow 0.9 m long. A water tank tower nearby is 24 m tall. How long is the tower’s shadow at that moment?

Class 10Triangles (Similarity)Geometry — Similarity
  • A32 m
  • B21.6 m
  • C28.8 m
  • D18 m

Step-by-Step Solution

The sun’ rays make equal angles, so the two triangles are similar: , giving m. 32 m comes from turning the ratio upside down ; 21.6 m and 28.8 m come from multiplying 24 by 0.9 or by 1.2 without dividing — the height and the shadow of the rod must appear on the same side of the fraction as the height and the shadow of the tower.
Answer: D) 18 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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