ABCD is a parallelogram in which diagonals AC and BD intersect at O If E F G and H are the mid point...........

Quantitative Aptitude ( CCS) Mensuration 2D

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

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Explanation:

In Δ OAB
Mid-point of OA = E
Mid-Point of OB = H
∴ EH || AB and HE = 1/2AB
Ref: Mid Point Theorem which says that the line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the length of the third side.
Similarly, HG = 1/2BC
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.