Question

In △ABC, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 19 cm, BC = 14 cm and AB = 29 cm. Find the perimeter of quadrilateral ARPQ. PLEAS GIVE A CLEAR EXPLANATION

Answer 1

Answer:

⇒ In △ABC, R and P are the mid-points of AB and BC

∴ RP∥AC, RP=

2

1

AC [ By mid-point theorem ]

In a quadrilateral RPQA,

⇒ RP∥AQ,RP=AQ

∴ RPQA is a parallelogram

⇒ AR=

2

1

AB

∴ AR=

2

1

×30=15cm

⇒ AR=PQ=15cm [ Since, opposite sides are equal ]

⇒ RP=

2

1

AC=

2

1

×21=10.5cm [ Since, opposite sides are equal ]

⇒ Perimeter of ARPQ=AR+QP+RP+AQ

=15+15+10.5+10.5

=51cm

∴ Perimeter of ARPQ is 51cm

Answer 2

Answer:

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