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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.
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Solution
In ΔABC
R and P are the midpoint 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
∴RPQA is a parallelogram
AR = `1/2` AB = `1/2 ` × 30 = 15cm
AR = QP = 15 [ ∵ Opposite sides are equal]
⇒ RP = `1/2` AC = `1/2` × 21 = 10 .5cm [ ∵ Opposite sides are equal]
Now,
Perimeter of ARPQ = AR + QP + RP + AQ
= 15 +15 +10.5 +10.5
= 51cm
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