Q. 29

ABCD is a trapezium in which AB||DC. M and N are the mid-points of AD and BC respectively, If AB=12cm, MN=14 cm, then CD=A. 10 cmB. 12 cmC. 14 cmD. 16 cm

Construction: Join A to C

Mark the intersection point of AC and MN as O

Now, M and N are mid points of the non-parallel of a trapezium

Therefore,

MN || AB || DC

So,

MO || BC

And,

M is a mid-point of AD

Therefore,

MO= BC

Similarly,

NO = AB

Therefore,

MN = MO + NO

= (AB + CD)

But,

MN = 14 cm

Hence,

(AB + CD) = 14 cm

12 + CD = 28

CD = 16 cm

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