SSC CGL 19 Oct 2014 Shift 2 Paper

Question : 135 of 200

Marks: +1, -0

ABCD is a parallelogram in which diagonals AC and BD intersect at O. If E, F, G and H are the mid points of AO, DO, CO and BO respectively, then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is

1 : 4
2 : 3
1 : 2
1 : 3

Validate

Solution:

In Δ OAB,
Mid-point of OA = E
Mid-point of OB = H
∴ EH || AB and HE =

1/2

AB
Similarly, HG =

1/2

BC
FG =

1/2

CD and EF =

1/2

AD
∴ EH + HG + FG + EF
=

1/2

(AB + BC + CD + AD)
⇒ Perimeter of EFGH
=

1/2

× Perimeter of ABCD
∴ Required ratio = 1 : 2

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