Answer :

Step1: draw a line segment XY of the length of the perimeter of the triangle so here XY = 15 cm



Step2: Now from point X construct a line XZ of any length at any acute angle below XY



Step3: take any distance in compass and keeping the needle of the compass on point X cut an arc on line XZ and name that point X1. Keeping the distance in compass same keep the needle of the compass on point X1 and cut an arc on line XZ and mark that point as X2. By doing this we are diving the line XZ in equal parts. Divide line into 3+4+6 = 13 parts i.e. by repeating this process mark points to X13



Step4: join points X13 and Y



Step5: as the ratio is 3:4:6 consider 3 parts i.e. point X3 then 4 parts i.e. point X7 and then 6 parts i.e. point X13 construct lines from point X3 and X7 parallel to line YX13 intersecting line XY at points Q and R respectively



Step6: take distance XQ in compass keep the needle of compass on point Q and mark an arc above XY



Step7: take distance RY in compass keep the needle at point R and draw an arc intersecting the arc drawn in step6 mark the intersection point as point P. draw segments PQ and PR and required ΔPQR is ready



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