SOLUTION: Julie wants to build a sidewalk of uniform width around her garden. Her garden is rectangular, and its dimensions are 20 feet by 30 feet. She has enough pavers to cover 900 square

Algebra ->  Test -> SOLUTION: Julie wants to build a sidewalk of uniform width around her garden. Her garden is rectangular, and its dimensions are 20 feet by 30 feet. She has enough pavers to cover 900 square       Log On


   

Question 1032795: Julie wants to build a sidewalk of uniform width around her garden. Her garden is rectangular, and its dimensions are 20 feet by 30 feet. She has enough pavers to cover 900 square feet and wants to use all the pavers. Complete the following statement. Round to the nearest tenth. Julie should make the width of the sidewalk _ _ _ _ _ feet.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of sidewalk be x
..
Length of garden = 30 feet
Width = 20 in -600
Total area =
Area = 600 m^2
Area of border = 900 m^2
Length of picture+border= 30 + 2 x
width of picture+border = 20 + 2 x

( 30 + 2 x ) ( 20 + 2 x ) + -600 = 900

600 + 60 x + 40 x + 4 X^2 + -600 = 900
4 X^2 + 100 x + -900 = 0
Find the roots of the equation by quadratic formula
a= 4 b= 100 c= -900
b^2-4ac= 10000 - -14400
b^2-4ac= 24400 sqrt%28%0924400%09%29= 156.2
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -100 + 156.2 )/ 8
x1= 7.03
x2=( -100 -156.2 ) / 8
x2= -15.5
Ignore negative value
width of border 7.03 feet