Please help! Mrs. Meckley wants to build a swimming pool surrounded by a sidewalk of uniform width. How wide should the sidewalk be

Question

Mrs. Meckley wants to build a swimming pool surrounded by a sidewalk of uniform width. She wants the dimensions of the pool and sidewalk to be 26 meters by 20 meters. The pool has an area of 216 square meters. How wide should the sidewalk be?

 

I'm not really sure where to start with this problem. It also says to write a variable equation. The subject we are on is Quadratic Equations, but I can't quiet connect. Please help.

Answer 1

OK, we know the lenght and width of the total area is 26 by 20

 

and we know the sidewalk is uniform width so

 

let the width of the sidewalk = w

 

then the length of the pool is 26 - 2w and the width of the pool is 20 - 2w

 

so now we can create an equation

 

A=lw

 

216 = (26-2w)(20-2w)

 

216 = 520 - 92w + 4w²

 

4w² -92w + 304 = 0

 

divide by 4

 

w² - 23 + 76 = 0

 

(w-19)(w-4) = 0

 

w - 19 = 0

 

w = 19      this does not work as an aswer becasue 2w is bigger than the lenght or width

 

w - 4=0

 

w = 4    and this should work and this is the width of the walk around the pool

 

26 - 8 =18

20 - 8 = 12

 

18*12 = 216 (the area of the pool

 

Hope this helps

 

Answer 2

Hi Is,

 

You have the area of the pool (216m²) and you have total area of the pool and the walk way (26*20 = 520m²).

 

Now notice if you call the width of the sidewalk x then the area of the sidewalk expressed by:

 

w = 26 -2x  and L = 20 -2x as its sides      //to avoid double count the side with 26 is taken end to end where the side                                                    //with 20 is cut off from both sides

 

=> 2*(26 - 2x)*(20)*2*x = 304

 

Solve this quadratic equation and you got your answer 

 

I hope this helps. It's a bit too involved