Answer :

We have been given one of the side of triangle and the difference of the other two sides along with one of the angle of a triangle.

Steps of construction:


1. Draw a line segment XY large enough with the use of a ruler.



2. Locate points B and C on XY, such that BC = 5 cm.



3. Draw a line segment BZ sufficiently large such that CBZ = 40°; do this with the help of a protractor.



4. From the segment BZ, cut off the line segment BD such that BD = 2.8 cm (here, we have presumed AB – AC = BD), using a compass and a ruler.


With B as centre, set the compass at 2.8 cm length and draw a circle or semicircle or an arc, and name the point where it intersects at BZ as D.



5. Join CD.



6. Draw perpendicular bisector of CD and let it meet BD at A. For perpendicular bisector of CD, fix the compass at a length just more than the length of CD and draw circles or arcs on both sides of the line segment CD taking C and D as centres one by one.



7. Join AC.



Thus, ABC is the required triangle.


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