Liz has a rectangular garden with a walkway around the edge. with the walkway included the entire garden area has a 20 foot length and an 18 foot width. At the edge of the walkway it is twice as wide as it is at the edge of the width. The area of the garden itself without the walkways 200 ft.². How wide is each part of the walkway?

Question

Liz has a rectangular garden with a walkway around the edge. with the walkway included the entire garden area has a 20 foot length and an 18 foot width.  At the edge of the walkway it is twice as wide as it is at the edge of the width.  The area of the garden itself without the walkways 200 ft.².  How wide is each part of the walkway?

L=20-4x
W=16-2x
A= (20-4x)(16-2x)
A=320-40x-64x+8x²
A=8x²-104x+320
I used the quadratic formula and got x=15.57 ft or x=-2.57 ft.
So the width of the short side is 15.57 ft and the width of the long side is 31.14 ft

Reiny · Answer

I see so many things wrong here.

Why are you taking 16-2x, when according to your question it should be 18-2x

which is it?

You also completely ignored the fact that the whole garden has an area of 200 f^2

Where did it say that the area of the walkway is zero?
That is what you are saying by solving it
using the quadratic equation formula
(your x= 15.57) ???