Answer:
The dimensions of the garden are
Length [tex]25.5\ ft[/tex] and Width [tex]16.5\ ft[/tex]
Step-by-step explanation:
Let
x----> the length of the rectangular garden
y ---> the width of the rectangular garden
Aw ----> the area of the walkway
we know that
[tex]x=y+9[/tex] ----> equation A
[tex]Aw=(x+8)(y+8)-xy[/tex]
[tex]Aw=400\ ft^{2}[/tex]
so
[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex]
[tex]400=8x+8y+64[/tex] ----> equation B
Substitute equation A in equation B
[tex]400=8(y+9)+8y+64[/tex]
[tex]400=8y+72+8y+64[/tex]
[tex]400=16y+136[/tex]
[tex]16y=400-136[/tex]
[tex]y=16.5\ ft[/tex]
Find the value of x
[tex]x=16.5+9=25.5\ ft[/tex]
therefore
The dimensions of the garden are
Length [tex]25.5\ ft[/tex]
Width [tex]16.5\ ft[/tex]
