Question

A footpath of uniform width runs all around the outside of a rectangular field of $30m$ long and $24m$ wide. If the path occupies $360m^2$, find its width.

• A. $2$m
• B. $3$m
• C. $5$m
• D. $8$m

Answer 1

The correct option is B $3$m

Area of the rectangular field $=(30\times 24)sqcm$$=720sq.m$
Area of footpath+area of rectangle $=360+720$$=1080sq.m$
Let the width of footpath be $x$ m

Therefore,

Area of entire field $=(30+2x)(24+2x)$

Therefore,

$(30+2x)(24+2x)=1080$
$=>720+48x+60x+4x^2=1080$
$=>x^2+27x-90=0$
$=>x^2+30x-3x-90=0$
$=>x(x+30)-3(x+30)=0$
$=>(x+30)(x-3)=0$

$x=-30$ or, $x=3$

$x=-30$ is not possible

Therefore, $x=3$

Therefore, width $=3m$