Question

A rectangular garden 50 m long by 34 m wide is surrounded by a sand path of uniform width. Calculate the width of this path if it is known that it has an area of 540 cm2.

Answer 1

Considering a width x of the sand path, we have a larger rectangle of dimensions 50+2x by 34+2x, as indicated in the figure. Now, the area of the sand path is expressed.

$\boldsymbol{\sf{ (50+2x)(34+2x)-50\times 34=540\Longrightarrow\quad 0=4x^2+168x-540 }}$

           $\boldsymbol{\sf{ 0=4(x^2+42x-135)=4(x-3)(x+45) }}$

Therefore, the path is 3 m long.