Construct a triangle ABC, whose perimeter is 13.5 cm and whose base angles are 60° and 75 °.

Question

Philoid · Accepted Answer

Step1: construct a segment XY of length perimeter which is 13.5 cm

Step2: draw ray XP at angle 60° from point X and a ray XQ at 75° from point Y

Step3: draw angle bisectors using protractor of ∠X and ∠Y and mark their intersection point as A

Now we have to draw perpendicular bisector of line AX and AY

Step4: take any distance approximately by observation in compass greater than half of XA. Keep the needle of the compass on point A and mark arcs above and below XA and keeping the same distance in compass keep the needle on point X and cut the arcs as shown and join both the intersected arcs. Thus we have drawn the perpendicular bisector of AX. Mark the intersection point of the perpendicular bisector of AX and XY as point B

Step5: similarly draw perpendicular bisector of segment AY and mark the intersection point with XY as C join AB and AC and required ΔABC is ready