- A1 : 8
- B1 : 9
- C1 : 3
- D1 : 6
Step-by-Step Solution
ΔADE ~ ΔABC with side ratio AD/AB = , so area ratio = . Thus ar(ADE) : ar(ABC) = 1 : 9, and ar(trapezium) = 9 − 1 = 8 parts. Hence ar(ADE) : ar(DBCE) = 1 : 8.
Answer: A) 1 : 8
In ΔABC, DE ∥ BC. If AD = 2 cm and AB = 6 cm, find the ratio of the area of ΔADE to the area of trapezium DBCE.
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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