SOLUTION: A resort's enormous rectangular pool is 500 meters wide and 250 meters long. A contractor is hired to construct a brick walkway around the pool with an area of 1504 m^2?. What are

Question 1194635: A resort's enormous rectangular pool is 500 meters wide and 250 meters long. A contractor is
hired to construct a brick walkway around the pool with an area of 1504 m^2?. What are the roots
of the working equation?
Found 3 solutions by Alan3354, greenestamps, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A resort's enormous rectangular pool is 500 meters wide and 250 meters long. A contractor is hired to construct a brick walkway around the pool with an area of 1504 m^2?.
What are the roots of the working equation?
==============
No "working equation" is given.
If you want to find the width of the walkway:
----
Pool area = 250*500 = 125000 sq meters
x = width of walkway
Area of pool and walkway = 125000+1504 = 126504
(250+x)*(500+x) = 126504
x^2 + 750x + 125000 = 125604
x^2 + 750x - 1504 = 0
x = 2 meters added to length and width
---> walkway is 1 meter wide
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Finding the width of the walkway (which SEEMS to be the objective) is much easier using common sense than with formal algebra.

The sections of the walkway are two sections 500 by x meters, two sections 250 by x meters, and four section x by x meters. With a total walkway area of 1504 meters, that gives us

Simple observation shows that x=1.

But the problem doesn't ask us to find the width of the walkway; it asks us what the roots are of the "working equation".

If we use the preceding discussion to form the "working equation", we have

ANSWER: The roots are x=-376 and x=1

A more standard way of setting up the problem leads to the same "working equation" by a different path.

The area of the walkway is the area of (pool plus walkway), minus the area of the pool:

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A resort's enormous rectangular pool is 500 meters wide and 250 meters long.
A contractor is hired to construct a brick walkway around the pool with an area of 1504 m^2.
What are the roots of the working equation?
~~~~~~~~~~~~~~~~~~~~

If x is the uniform width of the walkway around the rectangular pool, then the area equation is (500+2x)*(250+2x) = 500*250 + 1504, or 500*250 + 1500x + 4x^2 = 500*250 + 1504 4x^2 + 1500x - 1504 = 0 x^2 + 375x - 376 = 0 (x-1)*(x+376) = 0. The roots are x= 1 and x= -376: one positive and one negative. As a possible solution, we accept the positive root and reject the negative one.

Solved, answered and explained.

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

If you want to see many other similar (and different) 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.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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