The width of the walkway is: 3 feet
Step-by-step explanation:
Given
Length of pool = 20 feet
width of pool = 40 feet
Let x be the width of the side walkway
Then the length with walkway will be: 20+2x
Width with walkway will be: 40+2x
Then total area with walkway: [tex](20+2x)(40+2x)[/tex]
so,
[tex]Area\ with\ walkway - area\ of\ swimming\ pool=area\ of\ walkway\\(20+2x)(40+2x)-(20)(40)=396\\800+40x+80x+4x^2-800=396\\120x+4x^2=396\\4x^2+120x-396=0[/tex]
Dividing both sides by 4
[tex]x^2+30x-99=0\\x^2+33x-3x-99=0\\x(x+33)-3(x+33)=0\\(x+33)(x-3) = 0\\x-3=0 => x=3\\x+33=0 => x=-33[/tex]
As the measurement of length cannot be negative, we will only consider the positive value.
Hence,
The width of the walkway is: 3 feet
Keywords: Rectangle, Area
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