document.write( "Question 200274: A 4 meter by 6 meter rug covers half the floor area of a room and leaves a uniform strip of base floor around the edges. That are the dimensions of the room?\r
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document.write( "(4*6)(2)=n I am not sure what the correct equation is for this problem. \n" );
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Algebra.Com's Answer #150595 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! A 4 meter by 6 meter rug covers half the floor area of a room and leaves \n" ); document.write( " a uniform strip of base floor around the edges. \n" ); document.write( "That are the dimensions of the room? \n" ); document.write( ": \n" ); document.write( "Find the area of the rug: 4 * 6 = 24 sq/m \n" ); document.write( "Find the area of the floor: 2 * 24 = 48 sq/m (twice the rug area) \n" ); document.write( ": \n" ); document.write( "Let x = the width of the uniform strip around the rug \n" ); document.write( ": \n" ); document.write( "Room length * room width = 48 sq./m \n" ); document.write( "(2x+6) * (2x+4) = 48 \n" ); document.write( "FOIL \n" ); document.write( "4x^2 + 8x + 12x + 24 = 48 \n" ); document.write( ": \n" ); document.write( "4x^2 + 20x + 24 - 48 = 0 \n" ); document.write( ": \n" ); document.write( "4x^2 + 20x - 24 = 0; our old friend the quadratic equatio16 \n" ); document.write( ": \n" ); document.write( "Simplify, divide by 4: \n" ); document.write( "x^2 + 5x - 6 = 0 \n" ); document.write( ": \n" ); document.write( "Factor \n" ); document.write( "(x + 6)(x - 1) = 0 \n" ); document.write( ": \n" ); document.write( "x = +1 m is the width of the uniform strip, increases the dimensions by 2 m \n" ); document.write( "therefore \n" ); document.write( "6+2 = 8 m is the room length \n" ); document.write( "and \n" ); document.write( "4+2 = 6 m is the room width \n" ); document.write( " \n" ); document.write( " |