PUMPA - THE SMART LEARNING APP

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Draw a line segment $$QR = 6 \ cm$$.
Draw a perpendicular bisector $$AB$$ of line segment $$RS$$.
Take $$13 \ cm$$ as the radius, with $$Q$$ as centre, draw an arc that cuts $$QY$$ at $$S$$, then draw a line from $$R$$ to $$S$$ to connect the two points.
Mark a point $$P$$, where the perpendicular bisector intersects $$QS$$, then join $$PR$$.
Make $$\angle YQR = 45^\circ$$.
Construct a triangle $$PQR$$ in which $$QR = 6 \ cm$$, $$\angle Q = 45^\circ$$ and $$PQ + PR = 13 \ cm$$.

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Thus, $$PQR$$ is the required triangle.