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

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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.

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