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in Parallelograms by (26.9k points)
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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 cm 

B. 12 cm 

C. 14 cm 

D. 16 cm

1 Answer

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by (27.3k points)
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Best answer

Option : (D)

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 = \(\frac{1}{2}\)BC 

Similarly, 

NO = \(\frac{1}{2}\)AB 

Therefore, 

MN = MO + NO 

= \(\frac{1}{2}\)(AB + CD) 

But, 

MN = 14 cm 

Hence, 

\(\frac{1}{2}\)(AB + CD) = 14 cm 

12 + CD = 28 

CD = 16 cm

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