Question

Using ruler and compasses only, construct a Δ ABC from the following data:
AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Answer 1

We are asked to draw triangle ABC whose base angles are 60° and 45° and its perimeter is 12 cm

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw DE of length 12 cm.

STEP2: Construct ∠EDP =∠C = 60° and ∠DER =∠B = 45°, using regular methods.

STEP3: Draw the angle bisectors of ∠EDP and ∠DER and mark their point of intersection as A.

STEP4: Draw the perpendicular bisectors of AE and AD. They meet DE at point B and Point C respectively.

STEP5: Draw AB and AC to get the required ΔABC.