document.write( "Question 79323: A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the lenght of a side of the rug and the lenght of a side of the room is 17 feet. Find the dimensions of the room.\r
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Algebra.Com's Answer #56929 by ankor@dixie-net.com(22740)\"\" \"About 
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A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the length of a side of the rug and the length of a side of the room is 17 feet. Find the dimensions of the room.
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\n" ); document.write( "Let x = 1 side of the room
\n" ); document.write( "Then x^2 = area of the room
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\n" ); document.write( "Let (17-x) = 1 side of the square rug
\n" ); document.write( "Then (17-x)^2 = area of the rug
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\n" ); document.write( "Room area - rug area = 51 sq/ft
\n" ); document.write( "x^2 - (17-x)^2 = 51
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\n" ); document.write( "x^2 - (289 - 34x + x^2) = 51; FOILed (17-x)(17-x)
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\n" ); document.write( "x^2 - 289 + 34x - x^2 = 51; Removed the brackets, changed the signs
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\n" ); document.write( "34x = 51 + 289; x^2's eliminated, added 289 to both sides
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\n" ); document.write( "34x = 340
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\n" ); document.write( "x = 340/34
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\n" ); document.write( "x = 10 ft is the side of the room
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\n" ); document.write( "17 - 10 = 7 ft is the side of the rug
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\n" ); document.write( "Check, room area - rug area
\n" ); document.write( "10^2 - 7^2 = 51
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