Question
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?
Answers
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
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
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