Question

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

Answer 1

Answer:

Step-by-step explanation:

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Here is the correct question:

ABCD is a trapezium in which AB || DC and AD= BC. If P,Q,R,S be respectively the mid-points of BA, BD and CD, CA, then PQRS is a __________.

Here is your answer:

First of all we will draw a quadrilateral ABCD with AD = BC and join AC, BD, P,Q,R,S are the mid points of AB, AC, CD and BD respectively.

In the triangle ABC, P and Q are mid points of AB and AC respectively.

PQ || BC and PQ = 1/2

BC .. (1)

In ΔADC, QR = 1/2

AD = 1/2

BC ... (2)

Now we will consider ΔBCD,

SR = 1/2

BC.. (3)

In ΔABD,

PS = 1/2

AD = 1/2

BC.. (4)

So from (1), (2), (3) and (4)

we will get

PQ = QR = SR = PS

All sides are equal so PQRS is a Rhombus.

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Answer 2

Answer:

16 cm

Step-by-step explanation:

In trapezium AB || DC

M and N are mid-points of sides AD and BC and MN are joined

AB = 12 cm, MN = 14 cm

∵ MN = 12(AB + CD)

⇒ 2MN = AB + CD

⇒ 2 x 14 = 12 + CD

CD = 2 x 14 – 12 = 28 – 12

= 16 cm