a farmer fences off a small.rectangular plot of land thay is 60 feet by 100 feet. within that area, a garden is planted and surrounded by a walkway of uniform width. how wide is the walkway if the area of the planted area is one half of the area of the plot?

Answer 1

let the width of the pathway be x ft

width of garden = 60-2x , x < 30
length of garden = 100-2x ,

area of garden = (60-2x)(100-2x)
= 6000 - 320x + 4x^2

area of plot = 6000
half of plot = 3000

4x^2 - 320x + 6000 = 3000
x^2 - 80x + 750 = 0
I will complete the square:
x^2 - 80x + 1600 = -750 + 1600
(x-40)^2 = 850
x-40 = ±√850 = ±29.155
x = ±29.155 + 40
= 69.155 ---> outside our restriction
or
x = 10.845