Question

# Question 11 If ΔABC∼ΔQRP,ar(ΔABC)ar(ΔPQR)=94, AB = 18 cm and BC = 15cm, then PR is equal to (A) 10 cm (B) 12 cm (C)  203 cm (D)​​​​​​​ 8cm

Solution

## (A) 10 cm Given, in ΔABC∼ΔQRP,AB=18cm and BC=15cm We know  that, the ratio of area of two similar triangles is equal to the ratio of square of their corresponding sides. ∴ ar(ΔABC)ar(ΔQRP)=(BC)2(RP)2 But given, ar(ΔABC)ar(ΔPQR)=94    [given] ⇒ (15)2(RP)2=94  [∵ BC=15cm, given] ⇒ (RP)2=225×49=100 ∴ RP=10cm

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