Q16 of 24 Page 157

In the triangle ABC, the midpoints of BC, CA and AB are P, Q and R respectively; if AC = 21 cm, BC = 29 cm. and AB = 30 cm, then let us write the perimeter of the quadrilateral ARPQ.


If R, Q and P are the midpoints of AB, AC and BC, and by applying the theorem:-


The line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it, we get


and PQ||AR


Also, and PR || AQ


Since the above conditions are sufficient for a parallelogram, therefore ARPQ is a parallelogram.


Perimeter of parallelogram ARPQ = (2×AR) + (2×AQ)


⇒ Perimeter = AB + AC = 30 + 21 = 51 cm


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