document.write( "Question 132621: A square lawn is surrounded by a walk one metre wide. If the area of the walk is equal to half the area of the lawn,what are the dimensions of the lawn??? \n" ); document.write( "
Algebra.Com's Answer #96990 by checkley71(8403)\"\" \"About 
You can put this solution on YOUR website!
LET X BE THE LAWN SIDE MEASUREMENT.
\n" ); document.write( "X^2=THE LAWN AREA.
\n" ); document.write( "(X+2)^2-X^2=X^2/2 TOTAL AREA [(X+2)^2] MINUS THE LAWN AREA [X^2] = 1/2 THE LAWN AREA [X^2/2].
\n" ); document.write( "X^2+4X+4-X^2=X^2/2
\n" ); document.write( "4X+4=X^2/2
\n" ); document.write( "X^2=2(4X+4)
\n" ); document.write( "X^2=8X+8
\n" ); document.write( "X^2-8X-8=0
\n" ); document.write( "USING THE QUADRATIC EQUATION:\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" WE GET:
\n" ); document.write( "X=(8+-SQRT[-8^2-4*1*-8])/2*1
\n" ); document.write( "X=(8+-SQRT64+32])/2
\n" ); document.write( "X=(8+-SQRT96)/2
\n" ); document.write( "X=(8+-9.7979)/2
\n" ); document.write( "X=(8+9.7979)/2
\n" ); document.write( "X=17.7979/2
\n" ); document.write( "X=8.899 METERS FOR THE DIMENSION OF THE SQUARE.
\n" ); document.write( "PROOF:
\n" ); document.write( "(8.899+2)^2-8.899^2=8.899^2/2
\n" ); document.write( "10.899^2-79.192=79.192/2
\n" ); document.write( "118.788-79.192=39.596
\n" ); document.write( "39.596=39.596
\n" ); document.write( " \n" ); document.write( "
\n" );