Given:
Width of a garden = 10 feet
Length of the garden = 14 feet
Area of the garden and the walkway together = 396 square feet.
To find:
The width of the walkway.
Solution:
A cement walkway is added around the outside of the garden.
Let x be the width of the walkway.
The width of the garden with walkway = 10+2x
The length of the garden with walkway = 14+2x
Area of a rectangle is
[tex]Area=length\times width[/tex]
Area of garden and the walkway together is
[tex]Area=(14+2x)\times (10+2x)[/tex]
[tex]396=140+28x+20x+4x^2[/tex]
[tex]396=140+48x+4x^2[/tex]
[tex]396=4(35+12x+x^2)[/tex]
Divide both sides by 4.
[tex]99=35+12x+x^2[/tex]
[tex]0=35-99+12x+x^2[/tex]
[tex]0=-64+12x+x^2[/tex]
Splitting the middle term, we get
[tex]x^2+16x-4x-64=0[/tex]
[tex]x(x+16)-4(x+16)=0[/tex]
[tex](x+16)(x-4)=0[/tex]
Using zero product property, we get
[tex](x+16)=0\text{ and }(x-4)=0[/tex]
[tex]x=-16\text{ and }x=4[/tex]
Width of walkway cannot be negative. So, x=4.
Therefore, the width of the walkways is 4 feet.
Answer:
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Hope it helps
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