SOLUTION: The resort you work for has a rectangular pool that is 25 m by 14 m. They are installing a new deck of uniform width around the pool. When the deck is complete the total are of th

Question 1190012: The resort you work for has a rectangular pool that is 25 m by 14 m. They are installing a new deck of
uniform width around the pool. When the deck is complete the total are of the pool and deck will be
580 m2
How wide is the deck (from pool to edge), ie. The uniform width?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
pool is 25 x 14=350 m^2
So decking has 230 m^2 area
the uniform width is x
(25+x)(14+x)=350+39x+x^2=580
x^2+39x-230=0
x=(1/2)(-39+sqrt(1521+920); sqrt(2441)=49.41
=5.203 m is the deck width and the answer
the dimensions are 30.203 m x 19.203 m=579.99 m^2

Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
The resort you work for has a rectangular pool that is 25 m by 14 m. They are installing a new deck of
uniform width around the pool. When the deck is complete the total are of the pool and deck will be
580 m2
How wide is the deck (from pool to edge), ie. The uniform width?
~~~~~~~~~~~~~~~

            The solution and the answer in the post by @Boreal are incorrect.

            So I came to bring a correct solution.

After installing the deck of uniform wide x, the outer dimensions are (25+2x) by (14+2x) meters. So, the area equation is (25+2x)*(14+2x) = 580 square meters. Simplify this equation; reduce it to the standard form quadratic equation and find the solution 350 + 28x + 50x + 4x^2 = 580 4x^2 + 78x - 230 = 0 2x^2 + 39x - 115 = 0 = = = . Of the two roots, only positive one is the solution x = 2.602 meters (2.6 meters, approximately). ANSWER. The deck around has uniform width of 2.6 meters.

Solved.

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If you want 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.

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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