SOLUTION: I saw this problem in my textbook:
A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area is 576 square meters m
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A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area is 576 square meters m
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Question 327454: I saw this problem in my textbook:
A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area is 576 square meters more than the area of the pool, find the dimensions of the pool.
How do they get the answer? I've tried by making Total Area = x^2+6x+576, but have been unable to obtain the answer. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A rectangular pool is surrounded by a walk 4 meters wide.
The pool is 6 meters longer than its width.
If the total area is 576 square meters more than the area of the pool,
find the dimensions of the pool.
:
Let x = the width of the pool
then
(x+6) = length of the pool
:
Find the area (a) of the pool
a = x(x+6)
a = x^2 + 6x; area of the pool only
:
The dimensions of the area including the 4' walkway (add 8 to each dimension)
(x+8) = overall width
(x+14) = overall length
:
Find the area (A) including the 4m walkway
FOIL: (x+8)(x+14)
A = x^2 + 22x + 112; the total area
:
"If the total area is 576 square meters more than the area of the pool,"
(x^2 + 22x + 112) - (x^2 + 6x) = 576
remove the brackets
x^2 + 22x + 112 - x^2 - 6x = 576
results
22x - 6x = 576 - 112
:
16x = 464
x =
x = 29 m is the width of the pool
then
29 + 6 = 35 m is length
:
:
Check solution using x=29
29(29+6) = 1015 pool area
(29+8)(29+14) = 1591 overall area
1591 - 1015 = 576; confirms our solution
