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Question

Given: RS and PT are altitudes of ΔPQR
Then 



A

PQ×RQ=QT×QS

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B

PQ×QT=RQ×QS

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C

PQ×QS=RQ×QT

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D

PQ×RP=RQ×QS

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Solution

The correct option is A

PQ×QS=RQ×QT


In ΔPQT and ΔRQS,

PTQ=RSQ=90
(since RS and PT are altitudes)

PQT=RQS  
(common angle in both the triangles)

ΔPQTΔRQS   
(by AA similarity criterion)

PQRQ=QTQS

PQ×QS=RQ×QT


Mathematics

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