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D lies on AB of triangle ABC with AD = 3.5 cm and AB = 5 cm, and E lies on AC with AE = 4.9 cm and AC = 7 cm. Angle A is common and the two pairs of sides about it are proportional, so triangle ADE is similar to triangle ABC.
Find area(ADE) : area(ABC).

Class 10Areas of Similar TrianglesGeometry — Similarity
  • A7 : 10
  • B343 : 1000
  • C49 : 100
  • D49 : 51

Step-by-Step Solution

and , confirming a similarity ratio of 7 : 10. Area ratio = , i.e. 49 : 100. 7 : 10 stops at the side ratio, 49 : 51 compares with the rest of the triangle (DBCE) instead of the whole, and 343 : 1000 cubes it.
Answer: C) 49 : 100

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