In the diagram below, PR and ST intersect at Q such that angle QPT is congruent to angle SRQ . If PQ=9, 6, PT=6, TQ=5 and SQ=8 then which of the following is the length of SR?
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Given : In the diagram below, PR and ST intersect at Q such that angle QPT is congruent to angle SRQ . PQ=9, 6, PT=6, TQ=5 and SQ=8
To find : Length of SR
Solution:
PR and ST intersect at Q such that angle QPT is congruent to angle SRQ
in ΔPQT & ΔRQS
∠PQT = ∠SQR ( vertically opposite angles)
∠QPT = ∠QRS
=> ΔPQT ≈ ΔRQS
=> PQ/QR = QT/QS = PT/SR
=> 9/QR = 5/8 = 6/SR
5/8 = 6/SR
=> SR = 9.6
length of SR = 9.6
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