In `Delta ABC` the lines are drawn parallel to BC,CA and AB respectively through A,B and C intersecting at P, Q and R. Find the ration of perimeter of `Delta PQR` and `DeltaABC`

Explanation

Clearly, `ABCQ` and `ARBC` are parallelograms.
`:.BC=AQ` and `BC=AR`
`=>AQ=AR`
`=>A` is the mid-point of `QR`.
Similarly, `B` and `C` are the mid-points of `PR` and `PQ` respectively.
`:.AB=1/2PQ`
`BC=1/2QR`
`CA=1/2PR`
`=>PQ=2AB`
`QR=2BC`
`PR=2CA`
`=>PQ+QR+RP=2(AB+BC+CA)`
`=>`Perimeter of `/_\PQR=2`(Perimeter of `/_\ABC`)
Hence, the ratio is `1:2`.