Question

What is the length of MN?

58 cm
75 cm
88 cm
116 cm

Answer 1

The length of MN is 58 cm.

Explanation:

Given the figure in which

AM=MB, CN=NB

So, M and N are the mid point of AB and BC

∴ By mid point theorem which states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side of the triangle and half the length of third side.

⇒ MN is parallel to AC and also half of third side i.e AC

`MN=(1)/(2)AC=(1)/(2)* 116=58 cm`

Hence, the length of MN is 58 cm.

Thus , the length of MN is 58 cm.

Answer 2

The length of MN is 58 cm.

Explanation:

In the given figure we can see that AM = MB

So, M is the mid point of AB.

Also, BN = NC ( Consider the given figure )

So, N is the mid point of BC.

Since M and N are the midpoints of AB and BC .

So, by mid segment theorem which sates that the segment joining the midpoints of any two sides of a triangle will be parallel to the third side of the triangle and half its length.

⇒ MN is parallel to AC

and

`MN = (1)/(2) AC`

`MN = (1)/(2) (116)`

`MN = 58 cm`

Thus , the length of MN is 58 cm.