Question

Construct a triangle PQR with its perimeter= 11cm and the base angles of 75degree and 30 degree.

Answer 1

The below given steps will be followed to construct the required triangle.

Step I: Draw a line segment AB of 11 cm.

(As PQ + QR + PR = 11 cm)

Step II: Construct an angle, ∠XAB, of 75 at point A and an angle, ∠YBA, of 30 at point B.

Step III: Bisect ∠XAB and∠YAB. Let these bisectors intersect each other at point P

Step IV: Draw perpendicular bisector ST of PA and UV of PB

Step V: Let ST intersect AB at Qand UV intersect AB at R.

Join PQ and QR

ΔPQR is the required triangle.