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Mid point

by shashank.ism » Mon Feb 08, 2010 9:12 am
Through T, the mid-point of the side QR of a triangle PQR, a straight line is to meet PQ produced to S and PR at U, so that PU = PS. If the length of UR = 2 cm, then the length of QS is

a) 3/2 cm
b) 7/2 cm
c) 5/2 cm
d) 3 cm
e) 2 cm
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by harsh.champ » Mon Feb 08, 2010 10:20 am
shashank.ism wrote:Through T, the mid-point of the side QR of a triangle PQR, a straight line is to meet PQ produced to S and PR at U, so that PU = PS. If the length of UR = 2 cm, then the length of QS is

a) 3/2 cm
b) 7/2 cm
c) 5/2 cm
d) 3 cm
e) 2 cm
The question seems difficult if we try to solve it by the formal technique.
But if we look closely , we find that UR = 2cm .Length of side PR = PU + UR = PS + UR = PS + 2 .
The other side will be definitely greater than 2.
So,we are left with b and c.
[spoiler]
My hunch is b since in QS we have to count an additonal length PS + PQ(?this is the side of the triangle)[/spoiler]

Can anybody suggest the proper method ??Am I missing something??
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