The diagram above shows a rectangular garden, bordered by a walkway consisting of white and gray rectangles. If all four of the gray rectangles have the same dimensions, and the garden measures 20 by 10 feet, what is the area of the walkway?The area of the walkway will result from \(TotArea-Gardern\), we need to define the area of the outer rectangle.

I will call \(x, y\) the sides of the small grey rectangle

(1) Each gray rectangle has area 12 square feet.\(xy=12\) could result from sides of \(1*12=12\) or \(2*6=12\) for example.

As the overall lenght of the sides of the rectangle change accordingly, this is not sufficient.

(2) The outer perimeter of the walkway is 88 feet.So half of the perimeter is the sum of the two sides of the outer rectangle: \(20+2x+10+2y=44\) or \(x+y=7\), this could be the case if \(x=2\) and \(y=5\) or \(x=1\) and \(y=6\),...

As we do not define a side, the area is not defined, not sufficient

1+2) \(xy=12\)

\(x+y=7\)

This is true if y=4 and x=3 (

or the opposite), but since we do not know which side of the rectangle they correspond, it's still not sufficient.

Example: side retangle \(20+2*3=26\), other side \(10+2*4=18\) \(Area_1=18*26\).

But if I switch x,y the result changesOr side retangle \(20+2*4=28\), other side \(10+2*3=16\) \(Area_2=28*16\), and \(Area_1\neq{}Area_2\)

E
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