Steps of Construction
(i) Draw BC = 7 cm.
(ii) Construct ∠YBC = 75°.
(iii) From ray BY, cut-off line segment BD = AB + BC = 13cm.
(iv) Join CD.
(v) Draw the perpendicular bisector of CD meeting BY at A.
(vi) Join AC to obtain the required triangle ABC.
Justification
Since A lies on the perpendicular bisector of CD.
∴ AC = AD
Now BD = 13 cm
⇒ BA + AD = 13 cm
⇒ BA + BC = 13cm
Hence, △ABC is the required triangle.