<PRE><B>Question 603175</B>
A rectangular swimming pool with a deck 5 feet wide is enclosed by a fence.
 The surface area of the pool is 572 square feet and the total area inclosed by the fence (including the pool and the deck) is 1,152 square feet.
 Find the dimensions of the pool.Pool is 5 foot away from all four sides.
:
Let L = Length of the pool
Let W = Width of the pool
then
The Walkway will add 10 ft to the Overall dimensions: (L+10) by (W+10)
:
Area of the pool
L*W = 572
:
Overall Area
(L+10)*(W+10) = 1152
LW + 10L + 10W + 100 - 1152 = 0
LW + 10L + 10W - 1052 = 0
Replace LW with 572
572 + 10L + 10W - 1052 = 0
10L + 10W - 480 = 0
Divide by 10
L + W - 48 = 0
L + W = 48
W = (48-L)
:
Replace W in the pool area equation
L(48-L) = 572
-L^2 + 48L - 572 = 0
Multiply by -1, makes it easier to factor
L^2 - 48L + 572 = 0
Factors to
(L-22)(L-26) = 0
Two solutions
L = 22, then W = 26
and
L = 26. then W = 22
;
we can say the pool is 26 by 22, confirm this: 26 * 22 = 572 sq/ft</PRE>