In the given triangle M, N and O are the respective mid points of BC, CA and AB. If AB = 60 cm, BC = 58 cm, AC = 42 cm, then what is the perimeter of quadrilateral AOMN?
plz answer it's urgent
Answers
Answer:
102 cm
Step-by-step explanation:
AB = 60 cm
AC = 42 cm
so, AN = 30 cm( N is in the mid of AC)
AO = 21 cm ( O is in the mid point of AB)
AN=OM ( opp sides of llgm)
OM=MN (opp sides of llgm )
so perimeter = 30 + 30 + 21 + 21
= 102 cm
I hope it helps you out
Given:
AB=60cm
BC=58cm
AC=42cm
To find:
The perimeter of the quadrilateral AOMN
Solution:
The perimeter of the quadrilateral AOMN is 102 cm.
We can find the perimeter by following the given steps-
We know that the points M, N, and O are the midpoints of BC, AC and AB.
This means that AO=OB, BM=MC, and AN=NC.
Since OM passes through the midpoints of AB and BC, OM is parallel to AC and equal to half of it. (Midpoint theorem)
OM=1/2 of AC
Similarly, MN is parallel to AB and equal to half of it.
MN=1/2 of AB
Now, in quadrilateral AOMN, the perimeter is the sum of all its sides.
The sides of AOMN are AO, OM, MN, and AN.
The perimeter of AOMN=AO+OM+MN+AN
AO=MN=1/2 of AB=1/2 of 60=30cm
OM=AN=1/2 of AC=1/2 of 42=21cm
On putting the values, we get
Perimeter of AOMN=30+21+30+21
=42+60
=102cm
Therefore, the perimeter of the quadrilateral AOMN is 102 cm.