Question

In trapezium ABCD, M and N are mid-points of AC and BD, and AB || CD. Find AB if CD = 16 cm, MN = 10 cm​

Answer 1

Step-by-step explanation:

ANSWER

Join BD, let BD and MN meet at Q. Since, M is the mid point of AD and N is the mid point of BC. So by mid point theorem, AB II MN IICD

In △, BDC and BQN,

∠B=∠B (Common)

∠BDC=∠BQN (Corresponding angles of parallel lines)

∠BCD=∠BNQ (Corresponding angles of parallel lines)

thus, △BDC∼△BQN

Thus,

QB

BD

=

QN

DC

2=

QN

DC

(Q is the mid point of BD)

QN=

2

1

DC

Similarly, QM=

2

1

AB

Hence, QM+QN=

2

1

(AB+DC)

MN=

2

1

(AB+CD)

Hence, 2×27=AB+20

AB=54−20=34cm

Answer 2

Step-by-step explanation:

ab is four centimetre ,I have verified