In a triangle, P, Q and R are the mid points of sides BC, CA and AB respectively.

Solution:

In ΔABC,

R and P are mid points of AB and BC

RP ∥ AC, RP = (1/2) AC [By Midpoint Theorem]

In a quadrilateral,

[A pair of side is parallel and equal]

RP ∥ AQ, RP = AQ

Therefore, RPQA is a parallelogram

⇒ AR = (1/2) AB = 1/2∗30 = 15 cm

AR = QP = 15 cm                 [Opposite sides are equal]

⇒ RP = (1/2) AC =1/2 ∗21 = 10.5 cm

RP = AQ = 10.5 cm             [Opposite sides are equal]

Now,

Perimeter of ARPQ = AR + QP + RP + AQ

= 15 + 15 + 10.5 + 10.5

= 51 cm