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Question -

In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.



Answer -

It is given that P, Q and R are the mid-points of BC, CA and AB respectively.
 
Also, we have  ,  and 
We need to find the perimeter of quadrilateral ARPQ
In  , P and R are the mid-points of CB and AB respectively.
Theorem states, the line segment joining the mid-points of any two sides of a traingle is parallel to the third side and equal to half of it.
Therefore, we get:
Similarly, we get
 
We have Q and R as the mid points of AC and AB respectively.
Therefore,
And
 
Perimeter of  
 
Hence, the perimeter of quadrilateral ARPQ is .

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