document.write( "Question 1128455: The owners of the rectangular swimming pool want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 74 square meters. How wide should they make the border? (Hint: The area of the larger rectangle minus the area of the smaller is the area of the border.)\r
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document.write( "Some more supporting information:
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document.write( "length= 25 + 2w (around the border)
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document.write( "width= 10 + 2w (around the border)\r
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document.write( "length= 25 meters (inside the swimming pool)
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document.write( "width= 10 meters (inside the swimming pool)
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Algebra.Com's Answer #745072 by llamdot(2)![]() ![]() ![]() You can put this solution on YOUR website! Hi ikelyn. I wasn't clear on the wording of the problem. My biggest apologies for that. \r \n" ); document.write( "\n" ); document.write( "This word problem came with a picture showing the measurements, so I am at fault for that. \r \n" ); document.write( "\n" ); document.write( "But nevertheless, I was able to solve the word problem, and will reword the original word problem below in much clearer terms, with explanation on how I came to the solution:\r \n" ); document.write( "\n" ); document.write( "\"The owners of the rectangular swimming pool in the illustration want to surround the pool with a crushed-stone border of uniform width. They have enough stone to cover 74 square meters. How wide should they make the border? (Hint: The area of the larger rectangle minus the area of the smaller is the area of the border.) Assume a = 25 m and b = 10 m.\"\r \n" ); document.write( "\n" ); document.write( "a+2w outside \n" ); document.write( "b+2w outside \n" ); document.write( "\n" ); document.write( "a and b = inside \n" ); document.write( "\n" ); document.write( "(a + 2w)(b + 2w) - ab = 74\r \n" ); document.write( "\n" ); document.write( "a = \n" ); document.write( "b = 8 m\r \n" ); document.write( "\n" ); document.write( "w > 0\r \n" ); document.write( "\n" ); document.write( "(25 + 2w) (10 + 2w)- 25 (10) = 74\r \n" ); document.write( "\n" ); document.write( "250 + 50w + 20w +4w^2 - 250 = 74\r \n" ); document.write( "\n" ); document.write( "4w^2 + 70w = 74\r \n" ); document.write( "\n" ); document.write( "4w^2 + 70w - 74 = 0\r \n" ); document.write( "\n" ); document.write( "Upon factoring the equation, came up with -37 / 2 , and 1. Forget the negative answer, the focus is on positive answer. \r \n" ); document.write( "\n" ); document.write( "Therefore, 1 meter wide is the answer.\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |