Question

construct angle ABC such that BC=8cm,angle B=45°,AB-AC=3.5cm

Answer 1

Given  BC = 8 cm.   ∠B = 45°.   AB - AC = 3.5 cm.

1) Draw a Horizontal line and mark  BC = 8.0 cm using a ruler.

2) Draw a line BE inclined at an angle (B =) ∠45° with BC.  This can be
    drawn by drawing a perpendicular line and then bisecting that angle.

3) Mark BD = 3.5 cm from B on this line BE.
    
4) Join DC.  Draw the perpendicular bisector FG of DC using the
    standard procedure.

5) Intersection of FG and BE gives the point A.

6) Join AC to complete triangle ABC.

Answer 2

Steps of construction :-

1) Draw base BC of length 8cm

2) Now let's draw B angle = 45 degrees
Let the day be BX

3) Open the compass to length AB-AC = 3.5 cm

Note : Since AB -AC = 3.5cm is positive So BD will be above line BC

From point B as center cut an arc on ray BX
Let the arc intersect BX at D

4) Join CD

5) Now we will draw perpendicular bisector of CD

6) Mark point A where perpendicular bisector intersects BD

7) Join AC

Therefore ∆ ABC is the required triangle.

Hope it helps you !!!

In the above attachments, First picture belongs to 2nd step, Second picture belongs to 4th step and Third picture belongs to 7th step.