Construct a triangle ABC in which BC = 8cm, ∠B = 45° and AB – AC = 3.5 cm.

Steps of construction
(i) Draw a line segment BC = 8 cm.
(ii) At point B, Using ruler and compass, draw an angle ∠CBX = 45°.
(iii) Taking B as centre and radius 3.5 cm, mark an arc, which intersects AX at D.
(iv) Jion CD and draw a perpendicular bisector (MN) of CD, which intersects at BD produced at A.
(v) join AC.
(vi) Triangle ABC is the required triangle.
Justification
Point A lies on the perpendicular bisector of DC. So, AD = AC
Here, AB = BD – AD
⇒ AB = BD – AC [∵ AD = AC]