Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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)
Kindly press the Thank You button and indicate this as best answer if it answers your question correctly. Thanks.
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
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.