1. In fig. PS = 2, SQ=6 QR = 5, PT = * & TR = y. then find the pair of value of x&y
such that ST II side QR.
Answers
Given : PS = 2, SQ=6 QR = 5, PT = x & TR = y
To Find : the pair of value of x &y such that ST II side QR.
Solution:
Thales theorem ( BPT)
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
ST II QR
=> PS/SQ = PT / TR
=> 2 / 6 = x/y
=> 1/3 = x/ y
=> y = 3x
PR = PT + TR = x + 3x = 4x
in ΔPQR
PQ = PS + SQ = 2 + 6 = 8
QR = 5
PR = 4x
Sum of two sides of a triangle is > third side
=> 5 + 4x > 8
=> 4x > 3
also
5 + 8 > 4x
=> 13 > 4x
=> 3 < 4x < 13
=> x = 1 , 2 , 3 ( considering integral values only )
y = 3 , 6 , 9
the pair of value of x & y = ( 1 , 3) , ( 2 , 6) and ( 3, 9)
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