Question

A rectangular pool $20$ meters wide and $60$ meters long is surrounded by a walkway of uniform width. If the total area of the walkway is $516$ square meters, how wide, in meters, is the walkway?

Answer 1

A rectangular pool has length $l=60m$ & breadth $b=20m$.

It has a surrounding walkway of area $=516m^2$.

Area (pool) $=60\times 20=1200m^2$

Let us take the width of the walkway $=\frac{X}{2}$.

$\therefore$ The length as well as the breadth of the area (pool+walkway) will be increased by $X$

So the length $=l$ of the area (pool+walkway) $=(60+X)m$ and the breadth $=b=(20+X)m$

$\therefore$ Area (pool+walkway) $=l\times b=\left[\right(60+X)\times (20+X\left)\right]m^2.$

$\therefore$ Area (walkway) = Area (pool+walkway) - Area (pool)

$=(60+X)\times (20+X)-1200=516m^2$ ....(given)

$\Rightarrow X^2+80X-516=0$

$\Rightarrow X=-86$ or $X=6.$

We reject the negative value as $X$ is a length.

So $X=6m$.

Ans- The width of the walkway $=\frac{X}{2}=3m.$