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Question

In the figure, AC = 10cm, PC = 15cm, PQ = 12 cm, find PB.


A

6 cm

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B

7 cm

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C

8 cm

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D

9 cm

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Solution

The correct option is D

9 cm


In ΔABC and ΔPQC,PQC=ABC=90C=C (common angle)Therefore, ΔABCΔPQC by AA similarityACPC=ABPQ=BCQC1015=AB12=BCQCAB=8cmIn ΔABC,AB2+BC2=AC2102=82+BC2BC=6cmPB=PCBC=156=9cmHence, PB=9cm.


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