Question

In the adjoining figure a+b+c=​

Answer 1

Answer:

From the figure, it is given that, Through A,B and C lines are drawn parallel to BC,CA and AB respectively.

We have to show that 2(AB+BC+CA)=PQ+QR+RP

∵ AB∥RC and AR∥CB

Therefore, ABCR is a parallelogram.

⟹AB=CR and CB=AR (opposite sides of a parallelogram are equal) -------(1)

Similarly, ABPC is a parallelogram (∵AB∥CP and PB∥CA)

⟹AB=PC and AC=PB (opposite sides of a parallelogram are equal) -------(2)

Similarly, ACBQ is a parallelogram (∵BC∥AQ and AC∥BQ)

⟹AC=BQ and BC=AQ (opposite sides of a parallelogram are equal) --------(3)

By adding the equations (1), (2) and (3) we get,

AB+AB+BC+BC+AC+AC=PB+PC+CR+AR+BQ+AQ

2AB+2BC+2AC=PQ+QR+RP

By taking common we get,

2(AB+BC+AC)=PQ+QR+RP

Answer 2

Answer:

ur answer is in the attachment

hope it's helpful