SOLUTION: The owners of the rectangular swimming pool want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 74 square meters. How wide shoul

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The owners of the rectangular swimming pool want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 74 square meters. How wide shoul      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1128455: The owners of the rectangular swimming pool want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 74 square meters. How wide should they make the border? (Hint: The area of the larger rectangle minus the area of the smaller is the area of the border.)
Some more supporting information:
length= 25 + 2w (around the border)
width= 10 + 2w (around the border)
length= 25 meters (inside the swimming pool)
width= 10 meters (inside the swimming pool)
Found 2 solutions by ikleyn, llamdot:
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your post is uncompleted, since it does not provide input info about the dimensions of the pool.

Then you add this info L = 25 m, W = 10 m.

With this data the solution is as follows: 

    (25+2w)*(19+2w) - 25*10 = 74.        <<<---=== the area of the border is the difference of areas of two rectangles 


    25*19 + 50w + 38w + 4w^2 - 25*10 = 74


    4w^2 + 88w - 74 = 0


    2w^2 + 44w - 37 = 0

From this point, can you complete the solution on your own ?

You can use the quadratic formula to solve the last equation.


            Good luck and happy solving !


------------------

To see many other similar solved problems,  look into the lessons
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Cynthia Besch wants to buy a rug for a room
    - Problems on a circular pool and a walkway around it
in this site.

-----------------

Thanks for posting your solution.

I edited a bit your last post.

I am very glad that you made a step forward after my response and were able to complete the solution.

Your answer is correct, and your post clearly shows that you understand the solution in all details.


Again, I am very glad.

My congratulations !


Answer by llamdot(2) About Me  (Show Source):
You can put this solution on YOUR website!
Hi ikelyn. I wasn't clear on the wording of the problem. My biggest apologies for that.
This word problem came with a picture showing the measurements, so I am at fault for that.
But nevertheless, I was able to solve the word problem, and will reword the original word problem below in much clearer terms, with explanation on how I came to the solution:
"The owners of the rectangular swimming pool in the illustration want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 74 square meters. How wide should they make the border? (Hint: The area of the larger rectangle minus the area of the smaller is the area of the border.) Assume a = 25 m and b = 10 m."
a+2w outside highlight%28cross%28area%29%29 length
b+2w outside highlight%28cross%28area%29%29 width
a and b = inside highlight%28cross%28area%29%29 dimensions.
(a + 2w)(b + 2w) - ab = 74
a = highlight%28cross%2829%29%29 25 m
b = 8 m
w > 0
(25 + 2w) (10 + 2w)- 25 (10) = 74
250 + 50w + 20w +4w^2 - 250 = 74
4w^2 + 70w = 74
4w^2 + 70w - 74 = 0
Upon factoring the equation, came up with -37 / 2 , and 1. Forget the negative answer, the focus is on positive answer.
Therefore, 1 meter wide is the answer.