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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 the value of CD form the following choices is:

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10 cm

12 cm

14 cm

16 cm

answer is D.

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Detailed Solution

Given that,

A B C D

is a trapezium,

A B ‖ D C

, M and N are the mid-points of

A D

and

B C

and

A B = 12 c m, M N = 14

cm
Draw the figure.
Question Image

Join

A C

Midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.
Use mid-point theorem in

Δ A D C,

M O ‖ D C, M O = 12 D C … .. (1)

Similarly in

Δ A B C

N O ‖ A B, N O = 12 A B … . (2)

Substitute value of AB in (2).

N O = 12 (12) ⇒ N O = 6 cm

Calculate the value of

M O

.
Since

O

is a point on

M N

M O + N O = M N

… … . (3)

Substitute value of

N O, M N

in (3).

M O + 6 = 14 ⇒ M O = 14 − 6 ⇒ M O = 8 cm

Substitute the value of

M O

in (1).

8 = 12 D C ⇒ D C = 16 cm

Therefore, the value of CD is 16 cm.
Hence option 4) is correct.

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