In the given figure, T is a point on QR such that QT : TR = 3 : 5 and U is a point on PR such that PU : UR = 3 : 5, then the value of UT equals
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Given : T is a point on QR such that QT : TR = 3 : 5. U is a point on PR such that PU : UR = 3 : 5,
To Find : value of UT in terms of PQ
Solution:
QT : TR = 3 : 5
=> QT/TR = 3/5
=> QT/TR + 1 = 3/5 + 1
=> (QT + TR)/TR = (3 + 5)/5
=> QR/TR = 8/5
PU : UR = 3 : 5
=> PU/UR = 3/5
=> PU/UR + 1 = 3/5 + 1
=> PR/UR = 8/5
Comparing Δ UTR & ΔPQR
QR/TR = PR/UR = 8/5
∠R is common
Hence Δ UTR ≈ ΔPQR ( SAS criteria )
=> UT/PQ = UR/PR
=> UT/PQ = 5/8
=> UT = (5/8) PQ
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