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Step-by-Step Solution
The ratio of the areas of similar triangles is the square of the ratio of corresponding sides: . Area .
Answer: C)
The two triangles are similar, and the orange sides correspond. The smaller triangle has an area of . Find the area of the larger one.
Class 10Triangles (Similarity)Geometry — Similarity
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).
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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