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.
Answers
Given : In a triangle, P, Q and R are the mid-points of sides BC, CA and AB and AC = 21 cm, BC = 29 cm and AB = 30 cm.
In ΔABC,
R and P are the mid points of AB and BC.
By Mid-point Theorem :
RP || AC and RP = ½ AC
RP || AQ and RP = AQ
[½ AC = AQ]
Therefore, ARPQ is a parallelogram.
[One pair of opposite side are parallel and equal]
Now, AR = AB/2 = 30/2 = 15 cm
[AB = 30 cm ]
AR = QP = 15 cm
[ Opposite sides of a parallelogram are equal ]
And RP = AC/2 = 21/2 = 10.5 cm
[AC = 21 cm ]
RP = AQ = 10.5cm
[ Opposite sides of a parallelogram are equal ]
Now,
Perimeter of ARPQ = Sum of all sides
Perimeter of ARPQ = AR + QP + RP + AQ
Perimeter of ARPQ = 15 + 15 + 10.5 + 10.5
Perimeter of ARPQ = 51 cm
Hence , the Perimeter of quadrilateral is ARPQ is 51 cm.
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