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