Construct a triangle PQR, whose perimeter is15 cm and whose sides are in the ratio 3:4:6.

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