document.write( "Question 410593: you are planning a rectangular garden. Its length is twice its width x. You want a walkway 2ft wide around the garden.\r
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document.write( "a. Write an expression for the area of the garden and walk.
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document.write( "B. Write an expression for the area of the walk only.
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document.write( "c. You have enough gravel to cover 76ft^2 and want to use it all on the walk. How big should you make the garden? \n" );
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Algebra.Com's Answer #288857 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! you are planning a rectangular garden. \n" ); document.write( " Its length is twice its width x. \n" ); document.write( "You want a walkway 2ft wide around the garden. \n" ); document.write( ": \n" ); document.write( "x = the width of the garden \n" ); document.write( "then \n" ); document.write( "2x = the length \n" ); document.write( "and \n" ); document.write( "x(2x) = 2x^2; is the area of the garden \n" ); document.write( "; \n" ); document.write( "a. Write an expression for the area of the garden and walk. \n" ); document.write( "Area including the walk (a 2' walk all the way around, adds 4' to each dimension): \n" ); document.write( "A = (2x + 4)(x + 4) \n" ); document.write( "FOIL \n" ); document.write( "A = 2x^2 + 8x + 4x + 16 \n" ); document.write( "A = 2x^2 + 12x + 16, overall area \n" ); document.write( ": \n" ); document.write( "B. Write an expression for the area of the walk only. \n" ); document.write( "Overall area - garden area = walkway area \n" ); document.write( "2x^2 + 12x + 16 - 2x^2 = Walkway area \n" ); document.write( "Find the walkway area (A) \n" ); document.write( "A = 2x^2 - 2x^2 + 12x + 16 \n" ); document.write( "A = 12x + 16, walkway area \n" ); document.write( ": \n" ); document.write( "c. You have enough gravel to cover 76ft^2 and want to use it all on the walk. \n" ); document.write( " How big should you make the garden? \n" ); document.write( ": \n" ); document.write( "Replace A in the above equation with 76, find x which will give the dimension of the garden \n" ); document.write( "12x + 16 = 76 \n" ); document.write( "12x = 76 - 16 \n" ); document.write( "12x = 60 \n" ); document.write( "x = \n" ); document.write( "x = 5 ft is the width of the garden \n" ); document.write( "2(5) = 10 ft is the length \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "See if that makes sense \n" ); document.write( "(5+4)*(10+4) = 126 sq/ft overall area \n" ); document.write( "Garden: 5*10 = 50 sq/ft \n" ); document.write( "--------------------------- \n" ); document.write( "Walkway area 76 sq/ft \n" ); document.write( " \n" ); document.write( " |