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A swimming pool  20 m long and 10 m wide is surrounded by a deck of uniform width. The total area of the swimming pool and the deck is 704 m^2. Find the width of the deck.

Sagot :

Let x = width of the deck.
Therefore total area of pool : 
(10+2x)m*(20+2x)m = 704 m^2
( 200 + 20x + 40x + 4x^2 ) m^2 = 704 m^2
(200 + 60x + 4x^2)   = 704
 4x^2 + 60x = 704-200
 4x^2 + 60x = 504
 4x^2 + 60x - 504 = 0
4(x^2 + 15x - 126) = 0
(x+21) * (x-6) = 0
Therefore x, the deck's width is 6m (it can't be -21 as width is measured as a positive value)
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Lilith
[tex]S = 704 \ m^2 \\width \ of \ the \ deck - x \\ \\S=a \cdot b \\ \\ (10+2x)(20+2x) = 704 \\ \\ 200+20x +40x+4x^2-704 =0\\ \\4x^2 +60x -504=0\ \ /:4[/tex]
 
[tex]x^2+15x -126=0\\ \\a=1, \ b=15 , \ c= - 126 \\ \\\Delta =b^2-4ac = 15^2 -4\cdot1\cdot (-126) = 225 +504=729 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-15-\sqrt{729}}{2 }=\frac{ -15-27}{2}=\frac{-42}{2}=-21 \ can \ not\ be \ negative \\ \\x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-15+\sqrt{729}}{2 }=\frac{ -15+27}{2}= 6 \ m \\ \\ Answer : \ waist \ width \ is \ 6 \ m[/tex]


View image Lilith
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