SOLUTION: I really need help on this problem please. A smal city park consists of a rectangular lawn surrounded on all sides by a 330 m^2(meters squared) border of flowers 2.5 m wide. Fin

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I really need help on this problem please. A smal city park consists of a rectangular lawn surrounded on all sides by a 330 m^2(meters squared) border of flowers 2.5 m wide. Fin      Log On


   

Question 162231: I really need help on this problem please.
A smal city park consists of a rectangular lawn surrounded on all sides by a 330 m^2(meters squared) border of flowers 2.5 m wide. Find the area of the lawn is the entire park is 5 m longer than it is wide.
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem we are just subtracting the area of a large rectangle from a smaller one.

W=width of the park
L=W+5=Length of the park
Area of the park rectangle is A=W(W+5)
We know that the border all around is 2.5m
Thus the width of the lawn is w-2(2.5)=w-5
Thus the length of the lawn is w+5-2(2.5)=w
The equation is as follows=

Area of the park-Area of the lawn=area of the border=330m^2

W(W+5)-(W-5)W=330
W^2+5W-W^2+5W=330
10W=330
Divide both sides by 10
W=33
The dimensions of the park is 33m x38m
The dimensions of the lawn is 28m x33m
Let's double check our answer

33(38)-28(33)=
1254-924=330