Construct a triangle PQR, whose perimeter is 13 cm and whose sides are in the ratio 2:3:4.
Step1: draw a line segment XY of the length of the perimeter of the triangle so here XY = 13 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 2+3+4 = 9 parts i.e. by repeating this process mark points to X9
Step4: join points X9 and Y
Step5: as the ratio is 2:3:4 consider 2 parts i.e. point X2 then 3 parts i.e. point X5 and then 4 parts i.e. point X9 construct lines from point X2 and X5 parallel to line YX9 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
