10. In APQR, ZQ = 90°. If PQ:QR = 1:1, then PQ : PR = (1:2, 1:V2,V2:1)​

2 thoughts on “10. In APQR, ZQ = 90°. If PQ:QR = 1:1, then PQ : PR = (1:2, 1:V2,V2:1)​”

1. Answer:

   (i) Given:

   PQ = 8 cm

   QR = 6 cm

   PR = ?

   ∠PQR = 90°

   According to Pythagoras Theorem,

   (PR)2 = (PQ)2 + (QR)2

   PR2 = 82 + 62

   PR2 = 64 + 36

   PR2 = 100

   ∴ PR = √100 = 10 cm

   (ii) Given :

   PR = 34 cm

   QR = 30 cm

   PQ = ?

   ∠PQR = 90°

   According to Pythagoras Theorem,

   (PR)2 = (PQ)2 + (QR)2

   (34)2 = PQ2 + (30)2

   1156 = PQ2 + 900

   1156 – 900 = PQ2

   256 = PQ2

   ∴ PQ = 16 cm

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