SOLUTION: A small city park consists of a rectangular lawn surrounded on all sides by 330 meters squared border of flowers 2.5 m wide. Find the area od the lawn if the entire park is 5 m lon

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A small city park consists of a rectangular lawn surrounded on all sides by 330 meters squared border of flowers 2.5 m wide. Find the area od the lawn if the entire park is 5 m lon      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 173876: A small city park consists of a rectangular lawn surrounded on all sides by 330 meters squared border of flowers 2.5 m wide. Find the area od the lawn if the entire park is 5 m longer than it is wide.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A small city park consists of a rectangular lawn surrounded on all sides by
330 meters squared border of flowers 2.5 m wide.
Find the area of the lawn, if the entire park is 5 m longer than it is wide.
:
Let x = width of the entire park
then
(x+5) = Length of the entire park
therefore
x(x+5) = area of the entire park
:
Since the walkway is 2.5 m wide, we can say:
(x-5) = width of the lawn
and
(x+5)-5 = x; is the length of the lawn
therefore
x(x-5) = area of the lawn
:
We can say:
entire park area - lawn area = 330 (area of the border)
:
x(x+5) - x(x-5) = 330
:
x^2 + 5x - x^2 + 5x = 330
:
x^2 - x^2 + 5x + 5x = 330
:
10x = 330
;
x = 33 m is the width of the entire area
and
33 + 5 = 38 length of the entire area
:
Find the dimensions of the lawn
33 - 5 = 28 m width of the lawn
and
33 m = length of the lawn
:
:
Check solution by find the area of the entire park and the lawn
(38*33) - (33*28) =
1254 - 924 = 330