# A children`s park is 350 m long and 200 m wide. It is surrounded by a pathway of uniform width. suppose the total area of the park and pathway is 74464 sq. m How wide is the pathway?

2
by lancebalaopotpot

2014-07-13T20:16:39+08:00
A=LW
350x200=70 000  (this would be the area of the park alone)
we subtract this area to the overall are so it is 74464-70000= 4464
the area of the pathway must be 4464.
The lenghts are 350 and 200.the width would be x. there are two opposite pathways so we must multiply each by 2.
2(350x)+2(200x)=4464
700x+400x=4464
1100x=4464.. then we divide both sides by 1100
x=4.0581
2014-07-13T20:34:08+08:00
First let x be the width of the pathway
since the length of the park is 350 and there are two pathways in each side, then the length of the whole park is 350 +2x
since the width of the park is 200 and there are two pathways in each side, then the witdht of the whole park is 350 +2x
the are is 74 464 right? so we will equate this,
(200+2x)(350+2x)=74464 evaluate the equation and we will get the roots(x) which are  4 and - 279..since there are no distance that is negative the we will  get 4...x=width of the pathway=4

therefore, the width of the pathway is 4