Construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13 cm.

Steps of construction
(i) Draw a line segment BC = 7 cm.
(ii) Using ruler and compass, draw an angle ∠CBX = 75°.
(iii) Taking B as centre and 13 cm as radius, mark an arc on BX, which intersects at D.
(iv) Jion CD and draw a perpendicular bisector (PQ) of CD, which intersects BD 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]
⇒ AB + AC = BD