SOLUTION: a landscaper who just completed a rectangular flower garden measuring 11 ft. in length and 8 ft in width orders one cubic yd of premixed cement all of which is used to create a bor

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Question 548294: a landscaper who just completed a rectangular flower garden measuring 11 ft. in length and 8 ft in width orders one cubic yd of premixed cement all of which is used to create a border of uniform width around the garden if the border is to have a depth of 3 inches, how wide will the border be? (1 cubic yd=27 cubic ft)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the width of the sidewalk
length including sidewalk = 11+2x
width+sidewalk=8+2x
Area with sidewalk - area of garden = srea of sidewalk


Area of sidewalk = (11+2x)(8+2x)-88
Volume of sidewalk =((11+2x)(8+2x)-88)*1/4 = 27
(11+2x)(8+2x)-88= 108
88+22x+16x+4x^2-88=108
4x^2+38x-108=0
/2
2x^2+19x-54=0
Find the roots of the equation by quadratic formula

a= 2 ,b= 19 ,c= -54

b^2-4ac= 361 + 432
b^2-4ac= 793
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 28.16
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%2812%29
x1=( -19 + 28.16 )/ 4
x1= 2.29
x2=( -19 -28.16 ) / 4
x2= -11.79
Ignore negative value
width = 2.29 feet
m.ananth@hotmail.ca