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.
Found 3 solutions by mananth, ikleyn, timofer:
Answer by mananth(16949) 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


Answer by ikleyn(53618) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


In the post by @mananth, the value of x2 is determined by @mananth incorrectly
as -15.5.

The correct value for x2 is about -30.

For this problem, the precise value of x2 does not matter, since it is negative.

But I do not think, that your teacher will be glad by seeing wrong value in your solution.



Answer by timofer(144) About Me  (Show Source):
You can put this solution on YOUR website!
Simplest equation found after some setup and some steps looks like x%5E2%2B25x-225=0.
Expecting to use quadratic formula solution and take the one with the plus-square root.

x=%28-25%2Bsqrt%281525%29%29%2F2