In APQR, 2Q = 90°,Qs L PR,QS=12, SR= 8, Find PS.
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Given, ΔPQR in which ∠Q = 90°, QS ⊥ PR and PQ = 6 cm, PS = 4 cm In ΔSQP and ΔSRQ,
ANSWER
In triangles PQS and PQR
∠P is common to both.
and ∠PSQ=∠PQR
Triangles PQS and PQR are equiangular
∴
PQ
PS
=
QR
QS
or, PS=
QR
PQ⋅QS
...(i)
Again, triangles QRS and PQR are equiangular
∴
QR
SR
=
PQ
QS
or, SR=
PQ
QS⋅QR
...(ii)
From eqns. (i) and (ii)
SR
PS
=
QR
PQ⋅QS
⋅
QR⋅QS
PQ
=
QR
2
PQ
2
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