Correct Answer – Option 1 : 20 cm

Given:

ABCD is a trapezium, AB ∥ DC

M is mid-point of AD

N is mid-point of BC

AB = 14 cm

MN = 17 cm

Formula Used:

MN = 1/2 × (AB + CD)

In a trapezium AB ∥ DC

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

Calculation:

MN = 1/2 × (AB + CD)

⇒ 17 = 1/2 × (14 + CD)

⇒ 34 = 14 + CD

⇒ CD = 34 – 14

⇒ CD = 20 cm

∴ The length of CD is 20 cm.

Correct Answer – Option 2 : 61.75 cm

Given:

ABCD is a trapezium, AB ∥ DC

M is mid-point of AD

N is mid-point of BC

AB = 71.5 cm

CD = 52 cm

Formula Used:

MN = 1/2 × (AB + CD)

In a trapezium AB ∥ DC

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

Calculation:

MN = 1/2 × (AB + CD)

⇒ MN = 1/2 × (71.5 + 52)

⇒ MN = 1/2 × 123.5

⇒ MN = 61.75 cm

∴ The length of MN is 61.75 cm.

Correct Answer – Option 3 : 57.75 cm

Given:

ABCD is a trapezium, AB ∥ DC

M is mid-point of AD

N is mid-point of BC

AB = 40.25 cm

MN = 49 cm

Formula Used:

MN = 1/2 × (AB + CD)

In a trapezium AB ∥ DC

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

Calculation:

MN = 1/2 × (AB + CD)

⇒ 49 = 1/2 × (40.25 + CD)

⇒ 98 = 40.25 + CD

⇒ CD = 98 – 40.25

⇒ CD = 57.75 cm

∴ The length of CD is 57.75 cm.

Correct Answer – Option 2 : 12 cm

Given:

ABCD is a trapezium, AB ∥ DC

M is mid-point of AD

N is mid-point of BC

CD = 19 cm

MN = 15.5 cm

Formula Used:

MN = 1/2 × (AB + CD)

In a trapezium AB ∥ DC

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

Calculation:

MN = 1/2 × (AB + CD)

⇒ 15.5 = 1/2 × (AB + 19)

⇒ 31 = AB + 19

⇒ AB = 31 – 19

⇒ AB = 12 cm

∴ The length of AB is 12 cm.

Correct Answer – Option 3 : 15 cm

Given:

ABCD is a trapezium, AB ∥ DC

M is mid-point of AD

N is mid-point of BC

AB = 18 cm

CD = 12 cm

Formula Used:

MN = 1/2 × (AB + CD)

In a trapezium AB ∥ DC

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

Calculation:

MN = 1/2 × (AB + CD)

⇒ MN = 1/2 × (18 + 12)

⇒ MN = 1/2 × 30

⇒ MN = 15

∴ The length of MN is 15 cm.