Question 888369
Garden area is 40*20 square meters.


Let w = width of the walkway.


Combined area of the garden and walkway is (2w+40)(2w+20) square meters.


Twice the area of just the garden is 2*40*20.


Take the description from the second sentence and put into a meaningful equation:
<i>" combined area of the garden and walkway is twice the area of just the garden"</i>


{{{highlight_green((2w+40)(2w+20)=2*40*20)}}}
Solve this for w.
The obvious factored form as first shown here allows simplification by common factor elimination before going into multiplications.
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{{{2*2(w+20)(w+10)=2*2*2*10*20}}}
{{{(w+20)(w+10)=20*20}}}
{{{w^2+30w+200=400}}}
{{{w^2+30w=200}}}
{{{highlight_green(w^2+30w-200=0)}}}
? Factorable?
Discriminant, 900+4*200=900+800=1700=100*17, therefore not factorable.
{{{w=(-30+sqrt(100*17))/2}}}
{{{w=(-30+10sqrt(17))/2}}}
{{{highlight(w=5sqrt(17)-15)}}}
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5.6 meters