Answer:
The width of the sidewalk is 1 feet
Step-by-step explanation:
We are given
A rectangular garden is 6 feet by 4 feet
Let's assume width of the side of walk is x feet
Since, there is a sidewalk of uniform width around the garden
now, we can find width and height of the garden and side walk
L=6+2x
W=4+2x
now, we can find total area
Total area is
[tex]=L\times W[/tex]
now, we can plug values
[tex]=(6+2x)\times (4+2x)[/tex]
The area of the sidewalk and the garden together is 48 ft^2
so, we can set it equal and then we can solve for x
[tex](6+2x)\times (4+2x)=48[/tex]
[tex]24+20x+4x^2=48[/tex]
[tex]4x^2+20x-24=0[/tex]
we can factor out 4
[tex]4(x^2+5x-6)=0[/tex]
[tex](x+6)(x-1)=0[/tex]
[tex]x=-6,x=1[/tex]
we know that dimension can never be negative
so, we will only consider positive
[tex]x=1[/tex]
