You can
put this solution on YOUR website!SEE PROBLEM #89194
Original garden area is 30*20 or 600 sq ft
Let x=width of path
Now we'll divide the path up into 4 rectangles:
Two of the rectangles are 30 ft long and x ft wide and they have a combined area of: 2*30x or 60x sq ft
The other two rectangles are (20-2x) ft long and x ft wide and they have a combined area of 2*(20-2x)*x or 40x-4x^2 sq ft
Now we are basically told that the area of the path is (600-400)or 200 sq ft. So:
60x+40x-4x^2=200 subtract 200 from each side
60x+40x-4x^2-200=200-200 collect like terms
100x-4x^2-200=0 divide each term by -4
x^2-25x+50=0 quadratic in standard form. Solve using the quadratic formula:
Lets look at:
;
;
ft--------------------NO!
Lets look at the other value for x:
;
;
ft---------------------------Answer
CK
We'll see if the area of the path is 200 sq ft
2*30*(2.19)+2*(20-4.38)*2.19=
131.4+68.42=199.82 ~~~200 sq ft
We obviously have some round-off error that you can work on
Hope this helps----ptaylor
