Question

A path $900m^2$ of uniform width surrounds a rectangular field $45$ metres by $35$ metres. The width of the path is ............

Answer 1

Shaded area $=900m^2$
Area of the rectangular field $45\times 35=1575m^2$
$\therefore$ $(45+2x)(35+2x)=1575+900=2475$
$\therefore (45+2x)(35+2x)=55\times 45$

$\therefore x=5$