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Assertion (A): If two triangles are similar, their corresponding altitudes are in the same ratio as their corresponding sides. Reason (R): The ratio of the areas of two similar triangles equals the ratio of their corresponding sides. Choose the correct option.

Class 10Triangles (Similarity)Geometry — Similarity
  • ABoth A and R are true, and R explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

Corresponding altitudes of similar triangles are indeed in the ratio of sides, so A is true. But the area ratio equals the SQUARE of the side ratio, not the side ratio, so R is false.
Answer: C) A is true but R is false

Key idea: Areas of similar triangles

**Theorem**: The ratio of the areas of two similar triangles is equal to the SQUARE of the ratio of their corresponding sides.

If ΔABC ~ ΔDEF with scale factor , then
Area(ABC)/Area(DEF) = .

**Why**: area scales as length × length. If both length and breadth scale by , area scales by .

**Example**: Two similar triangles have corresponding sides in ratio 3:5. Area ratio = 9:25.

**Reverse**: if areas are in ratio 16:25, sides are in ratio 4:5 (square root).

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