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# Construct a $$\triangle{ABC}$$ in which BC = 7 cm, $$\angle{B}$$ = $$75^\circ$$ and AB + AC = 13cm.

Given: In $$\triangle{ABC}$$ in which BC = 7 cm, $$\angle{B}$$ = $$75^\circ$$ and AB + AC = 13cm.
Steps of construction:

1. Draw the base BC = 7 cm.

2. At the point B make an $$\angle{XBC}$$ = $$75^\circ$$.

3. Cut a line segment BD equal to AB + AC = 13 cm from the ray BX.

4. Join DC.

5. Make $$\angle{DCY}$$ = $$\angle{BDC}$$.

6. Let CY intersect BX at A.
Hence, ABC is the required triangle.