SOLUTION: A 8 yard by 10 yard swimming pool is surrounded by a deck of uniform width.the area of the deck is 72yd squared . Find the width of the deck

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Question 1150605: A 8 yard by 10 yard swimming pool is surrounded by a deck of uniform width.the area of the deck is 72yd squared . Find the width of the deck
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A 8 yard by 10 yard swimming pool is surrounded by a deck of uniform width.the area of the deck is 72yd squared . Find the width of the deck
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d = deck width
Area of pool & deck = (2d+8)*(2d+10)
Area of deck = (2d+8)*(2d+10) - 8*10 = 72
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

The area of 72 square yards is the difference of the area of the larger rectangle and the pool's area.


Let w be the uniform width of the deck.


Then the dimensions of the larger rectangle are  (8+2w) yards and (10+2w) yards, 

and its area is  (8+2w)*(10+2w).


Thus you have this equation

    (8+2w)*(10+2w) = 8*10 + 72.


Simplify it

    80 + 20w + 16w + 4w^2 = 80 + 72

    4w^2 + 36w - 72 = 0

     w^2 +  9w - 18 = 0


      =  = .


Only positive root makes sense  w =  = 1.685  yards.    ANSWER


CHECK.  (8+2*1.685)*(10+2*1.685) - 8*10 = 72.0169  very close to 72 square yards.   ! Correct !

Solved.

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Closely related lessons to it are 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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