SOLUTION: A pool is twice as long as it is wide and is surrounded by a walkway of uniform width of 1 foot. The combined area of the pool and the walkway is 400 square feet. Find the dimen

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Question 1189225: A pool is twice as long as it is wide and is surrounded by a walkway of uniform width of 1 foot. The combined area of the pool and the walkway is 400 square feet.
Find the dimensions of the pool and the area of the pool,
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions of the pool, 2x and x
Pool upper surface's area, 2x^2

Dimensions for the OUTER part of bordering walkway , 2x+2*1 and x+2*1

------------------------------------------------------------------
The combined area of the pool and the walkway is 400 square feet.
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cross%28%282x%2B1%29%28x%2B1%29=400%29
highlight_green%28%282x%2B2%2A1%29%28x%2B2%2A1%29=400%29

Not this -----
cross%282x%5E2%2B3x%2B1=400%29
.
.
.
cross%28x=6.352%29--------the width

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
A pool is twice as long as it is wide and is surrounded by a walkway of uniform width of 1 foot.
The combined area of the pool and the walkway is 400 square feet.
Find the dimensions of the pool and the area of the pool.
~~~~~~~~~~~~~~~~


            The starting equation, its solution and the answer all are incorrect in the post by @josgarithmetic.

            I came to bring a correct solution. 


Dimensions of the pool, 2x and x
Pool upper surface's area, 2x^2


Dimensions for the OUTER part of bordering walkway , 2x+2 and x+2


------------------------------------------------------------------
The combined area of the pool and the walkway is 400 square feet.
------------------------------------------------------------------


    (2x+2)(x+2) = 400

    ( x+1)*(x+2) = 200

    x^2+3x+2 = 200

    x^2 + 3x - 198 = 0


    x = %28-3%2Bsqrt%289%2B4%2A198%29%29%2F2

    x = %28-3%2Bsqrt%28801%29%29%2F2

    x = %28-3%2B28.30194%29%2F2

    x = 12.651--------the width

    2*12.651 = 25.30-------the length


CHECK.  (25.30+2)*(12.651+2) = 400 square feet.


ANSWER.  The dimensions of the pool are 12.651 ft and 25.30 ft.

         The area of the pool is 12.651*25.30 = 320 square feet.

Solved.

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To see many other similar solved problems,  look into the lesson
    - 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.