Solving Pool Dimensions - Length = 30 ft, Width = 60 ft

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In summary, after solving for the dimensions of the pool using the given information and equations, it was determined that the length of the pool is 28.5 feet and the width is 57 feet. This was obtained by subtracting the area of the walkway from the total area of the rectangular swimming pool and setting it equal to the equation for the area of the pool. The discrepancy between the given answer and the calculated answer may be due to rounding or a typo.
  • #1
bacon
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The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4 ft wide. If the area of the walk is 748 square feet, determine the dimensions of the pool.

A= the total area bounded by the outer edge of the surrounding walk
W= the area of the walk
P= the area of the pool
x= the length of the short side of the pool

A=P+W
P=x2x=[tex]2x^{2}[/tex]
W=748
A=(x+8)(2x+8)=[tex]2x^{2}+24x+64[/tex]=[tex]2x^{2}+748
[/tex]
solving for x gives x=28.5 feet and 2x=57 feet
The answer sheet says the dimensions are 30 and 60 feet.
Where am I going wrong?
Thanks for any replies.
 
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  • #2
Well, if you plug 30 and 60 back in, you get 784 so maybe it's a typo.

Or they rounded.
 
  • #3
Did you draw and label a picture?
 
  • #4
symbolipoint said:
Did you draw and label a picture?

Yes. I just don't know how to reproduce it in the post.
 
  • #5
bacon said:
Yes. I just don't know how to reproduce it in the post.

Good. I believe you and see now that some of what you showed indicated that you used a picture. I'm working on the exercise right now. Someone will probably write a response before I finish. So far, I'm looking at A of pool equals A of wholeRectangle minus A of walkway. I obtained 2x^2 = (x+8)(2x+8) - 748, and I'm not finished.
 
  • #6
bacon, in fact, I found the same results as you did: x=28.5, 2x=57
 

What are the dimensions of the pool?

The pool has a length of 30 feet and a width of 60 feet.

How do you calculate the area of the pool?

The area of the pool can be calculated by multiplying the length and width: 30 ft x 60 ft = 1800 square feet.

What is the volume of the pool?

The volume of the pool can be calculated by multiplying the area by the depth. If the depth of the pool is, for example, 5 feet, then the volume would be 1800 square feet x 5 feet = 9000 cubic feet.

How many gallons of water can the pool hold?

The number of gallons the pool can hold depends on the volume and shape of the pool. To calculate the number of gallons, divide the volume (in cubic feet) by 7.48. For example, a pool with a volume of 9000 cubic feet can hold approximately 1203 gallons of water.

What is the depth of the pool?

The depth of the pool is not specified in the given dimensions. Further information is needed to determine the depth of the pool.

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