Question

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

Options

• 10 cm

• 12 cm

• 14 cm

• 16 cm

Answer 1

The given trapezium ABCD can be drawn as follows:

Here, AB || CD.

M and N are the mid-points of AD and BC respectively.

We have AB = 12cm ,MN = 14cm.

We need to find CD.

Join MN to intersect AC at G.

We have AB || CD and a line MN formed by joining the mid-points of sides AD and BC.

Thus, we can say that MN || AB || CD

In  ΔADC M is the mid-point of AD and MG || CD

Therefore, G is the mid point of AC

By using the converse of mid-point theorem, we get:

 `MG = 1/2 CD`…… (i)

In ΔABC, N is the mid point of BC and GN || AB

By using the converse of mid-point theorem, we get:

 `GN = 1/2 AB` …… (ii)

Adding (i) and (ii),we get:

 `GN + MG = 1/2AB +1/2 CD`

 `MN = 1/2 (AB + CD)`…… (iii)

On substituting AB = 12cm and  MN = 14cm in (iii),we get:

          `14cm = 1/2(12cm + CD)`

           28cm = 12cm + CD

               CD = (28 - 12)cm

               CD = 16cm

Hence the correct choice is (d).