Question

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
​

Answer 1

Answer:

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