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Question

In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then PQ = ____.


A

4 cm

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B

6 cm

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C

8 cm

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D

9 cm

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Solution

The correct option is B

6 cm


In ΔPQB & ΔPDR

P=P (common)

PDR=PQB (corresponding angles)

ΔPDR ΔPQB (AA similarity)

PDPR=PQPB (corresponding sides)

PDPQ=PRPB ---- (1)

In ΔPQR & ΔPAB

P=P (common)

PQR=PAB (corresponding angles)

ΔPQR ΔPAB (AA similarity)

PQPR=PAPB (Corresponding sides)

PQPA=PRPB ---- (2)

From (1) & (2), we get

PDPQ=PQPAPQ2=PD×PAPQ2=4×9

PQ=6 cm


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