Question 104677
Area=length*width
____=30ft*40ft
____=1200 sq. ft

Let x= the width of the walkway

Then, the new length of the whole space is 40+2x and the new width is 30+2x

The total area, garden plus walkway, is to be 1800 sq. ft. So,

__________________________{{{(40+2x)*(30+2x)=1800}}}____________________________
____________________{{{40*(30+2x)+2x*(30+2x)=1800}}}____________________________
____________________{{{(1200+80x)+(60x+4x^2)=1800}}}____________________________
______________________{{{1200+(80x+60x)+4x^2=1800}}}____________________________
______________________{{{1200+140x+4x^2-1800=1800-1800}}}_______________________
__________________________{{{-600+140x+4x^2=0}}}________________________________
___________________________{{{4x^2+140x-600=0}}}________________________________
_______________________{{{(1/4)*(4x^2+140x-600)=(1/4)*0}}}______________________
_____________________________{{{x^2+35x-150=0}}}________________________________

By the quadratic formula,

{{{x=(-35+-sqrt(35^2-4*1*(-150)))/(2*1)}}}
{{{x=(-35+-sqrt(1225+600))/(2)}}}
{{{x=(-35+-sqrt(1825))/(2)}}}
{{{x=(-35+42.72)/(2)}}} or {{{x=(-35-42.72)/(2)}}}
{{{x=3.85}}} or {{{x=-38.6}}}

The negative result will not be ACCEPTED for there's no such things such as NEGATIVE LENGTH!


Therefore, the length must be 3.85 ft wide!


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