Question

ABC is a triangle through vertex A a line RQ is drawn parallel to side BC similarly PR and QP are the lines drawn through the vertex B and C parallel to AC and AB respectively to foam another triangle PQR. find the ratio of perimeter of Triangle ABC to that of triangle pqr​

Answer 1

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=½ PQ,BC= ½QR and CA½ PR

⇒PQ=2AB,QR=2BC and PR=2CA

⇒PQ+QR+RP=2(AB+BC+CA)

⇒ Perimeter of ΔPQR=2 (Perimeter of ΔABC)