Let the rectangle's length, $l$ be the semicircle's diameter, $2r$ and the rectangle's height/breadth/width, $h$ be the semicircle's radius, $r$ .

Area of semicircle : Area of smallest rectangle to contain that semicircle

$\frac{1}{2}$ $\pi$ $r^{2}$ : $h \times l$

Substitute

$\frac{1}{2}$ $\pi$ $r^{2}$ : $r \times 2r$

Simplify the ratios

$\frac{1}{2}$ $\pi$ $r^{2}$ : $2 r^{2}$

[remove $r^{2}$ from both sides]

$\frac{1}{2}$ $\pi$ : $2$

$\pi$ : $4$

$\pi$ : $x$

$x$ = $4$