We are asked to construct a triangle ABC in whichBC=3.4 cm, AB-AC=1.5 cm and ∠B = 45°.

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw BC of 3.4 cm.

STEP2: Produce BC to X at an angle of 45°.

STEP3: From the ray BX, cut BD of 1.5 cm.

STEP4: Draw segment DC.

STEP5: Draw the perpendicular bisector of DC, intersecting the ray BX at A

STEP6: Draw AC.

ABC is the required triangle.