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The PCTM Puzzle of the Week - Solutions

I see at least two answers to this problem.
the square numbers less than 30 are 1,4,9,16,25.
Because 16 and 25 work as dimensions, (25=5^2, 
16=4^2, 25-16=3^2)
we could stop at a 16x25 ft^2 pool.

But I KNOW that Mr. and Mrs. Gomez want the 
largest pool possible.
Thus, they realize that they could change the pool 
dimensions into
centimeters, giving a maximum of 609 cm x 914 
cm.
Mr. and Mrs. Gomez realize that they can make a 
pool that is:
576 cm x 900 cm, as 576=24^2, 900=30^2, 900-
576=324=18^2.
this is much larger than before, and they are both 
happy.

--Christophe
:*}

What I did was subtracted 1 away from 20 and 30 
until I came to a number that was a 
square number.  Those two numbers came to be, 16 
(from 20), and 25 (from 30).
16 was the square of 4, and 25 was the square of 5.  
I then subtracted 16 from 25 and
got 9, which was the square of 3.  9 was the 
difference from the pool and the yard.
I then multiplied 16 and 25 and got 400, which is 
the square of 20.
So...the answer to the problem (the dimensions of 
the pool)are,
16 by 25.

The pool would have to be 16 x 25 feet.  

16's square root is 4
25's square root is 5

25-16=9  9's sq. root is 3
 
the area would be 400 (16 x 25=400)
and 400's sq. root is 20.

I believe the best solution is:

Width : 25 = 5^2
Length: 16 = 4^2
Difference between width and length: 9 = 3^2
Area: 400 = 20^2

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