Draw a triangle $ABC$ in which $BC = 6 \, cm$,$CA = 5 \, cm$,and $AB = 4 \, cm$. Construct a triangle similar to it with a scale factor of $\frac{5}{3}$.

(A) $1.$ Draw a line segment $BC = 6 \, cm$.
$2.$ Taking $B$ and $C$ as centers,draw two arcs of radii $4 \, cm$ and $5 \, cm$ respectively,intersecting each other at $A$.
$3.$ Join $BA$ and $CA$. $\triangle ABC$ is the required triangle.
$4.$ From $B$,draw any ray $BX$ downwards making an acute angle with $BC$.
$5.$ Mark five points $B_1, B_2, B_3, B_4,$ and $B_5$ on $BX$ such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4 = B_4B_5$.
$6.$ Join $B_3C$. From $B_5$,draw $B_5M \parallel B_3C$ intersecting the extended line segment $BC$ at $M$.
$7.$ From point $M$,draw $MN \parallel CA$ intersecting the extended line segment $BA$ at $N$. Then,$\triangle NBM$ is the required triangle whose sides are $\frac{5}{3}$ times the corresponding sides of $\triangle ABC$.