Construct a triangle $ABC$ in which $BC = 7.5\, cm$,$\angle B = 45^{\circ}$ and $AB - AC = 4\, cm$.

(N/A) Steps of construction:
$1$. Draw a line segment $BC = 7.5\, cm$.
$2$. At point $B$,construct an angle $\angle XBC = 45^{\circ}$.
$3$. Cut a line segment $BD = 4\, cm$ from the ray $BX$.
$4$. Join $DC$.
$5$. Construct the perpendicular bisector of $DC$,which intersects $BD$ (extended if necessary) at point $A$.
$6$. Join $AC$. Thus,$\triangle ABC$ is the required triangle.