RRB Group-D Model Paper 17 with answers for online practice

Given:
Radius of semi-circle = r cm
Formula used:
Pythagoras theorem
${\mathit{H}}^2$ = ${\mathit{P}}^2+{\mathit{B}}^2$
Area of square = $\mathit{s}\mathit{i}\mathit{d}{\mathit{e}}^2$
Calculation:
Let the side of the square be ‘a’ cm
The maximum size square exists with side ‘r’ cm.
⇒ ${\mathit{H}}^2$ = ${\mathit{P}}^2+{\mathit{B}}^2$
⇒ ${\mathit{r}}^2$ = ${\mathit{a}}^2$ + ${\left(\frac{\mathit{a}}{2}\right)}^2$
⇒ ${\mathit{r}}^2$ = ${\mathit{a}}^2$ + $\frac{{\mathit{a}}^2}{4}$
⇒ ${\mathit{r}}^2$ = $5\frac{{\mathit{a}}^2}{4}$
⇒ a = $2\frac{\mathit{r}}{\sqrt{5}}$
∴ side of maximum size square is $2\frac{\mathit{r}}{\sqrt{5}}$ cm