Chapter: Similarity· Mathematics Part 2 (Geometry)

If \(\Delta ABC \sim \Delta PQR\) and \(\dfrac{A(\Delta ABC)}{A(\Delta PQR)} = \dfrac{16}{81}\), then AB : PQ = ?

A. 4 : 9

B. 16 : 81

C. 2 : 3

D. 9 : 4

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Answer: (A) 4 : 9

For similar triangles, \(\dfrac{A(\Delta ABC)}{A(\Delta PQR)} = \dfrac{AB^2}{PQ^2}\). So \(\dfrac{AB^2}{PQ^2} = \dfrac{16}{81}\) and \(\dfrac{AB}{PQ} = \dfrac{4}{9}\). Option (B) is the trap: it is the ratio of areas, not of sides.

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If \(\Delta ABC \sim \Delta PQR\) and \(\dfrac{A(\Delta ABC)}{A(\Delta PQR)} = \dfrac{16}{81}\), then AB : PQ = ?

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