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.
Answers
Answer:
answer of this is 51
Step-by-step explanation:
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:
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
