document.write( "Question 118067: The width of a rectangular gate is 2 meters(m) larger than its height. The diagonal brace measures the square root of 6. find the width and height. \n" ); document.write( "

Algebra.Com's Answer #86141 by josmiceli(19441) $\"\"$ $\"About$

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Use the pythagorean formula
\n" ); document.write( " $\"c%5E2+=+a%5E2+%2B+b%5E2\"$
\n" ); document.write( "where c is the diagonal, a is the width, b is the height
\n" ); document.write( " $\"%28sqrt%286%29%29%5E2+=+%28x+%2B+2%29%5E2+%2B+x%5E2\"$
\n" ); document.write( " $\"6+=+x%5E2+%2B+4x+%2B+4+%2B+x%5E2\"$
\n" ); document.write( " $\"2x%5E2+%2B+4x+-+2+=+0\"$
\n" ); document.write( " $\"x%5E2+%2B+2x+-+1+=+0\"$
\n" ); document.write( " $\"x%5E2+%2B+2x++=+1\"$
\n" ); document.write( "Complete the square. Take 1/2 of the coefficient of the $\"x\"$ term
\n" ); document.write( "square it, and add it to both sides
\n" ); document.write( " $\"x%5E2+%2B+2x+%2B+1+=+2\"$
\n" ); document.write( " $\"%28x+%2B+1%29%5E2+=+2\"$
\n" ); document.write( " $\"x+%2B+1+=+0+%2B-+sqrt%282%29\"$
\n" ); document.write( " $\"x+=+-1+%2B-+sqrt%282%29\"$
\n" ); document.write( " $\"x+=+-1+%2B+sqrt%282%29\"$ The other solution is negative,
\n" ); document.write( "so it must be rejected
\n" ); document.write( "The width is $\"x+%2B+2\"$ , so
\n" ); document.write( "width = $\"2+-+1+%2B+sqrt%282%29\"$
\n" ); document.write( "width = $\"1+%2B+sqrt%282%29\"$ answer
\n" ); document.write( "Height = $\"x\"$
\n" ); document.write( "height = $\"-1+%2B+sqrt%282%29\"$ answer
\n" ); document.write( "check
\n" ); document.write( " $\"%28sqrt%286%29%29%5E2+=+%28x+%2B+2%29%5E2+%2B+x%5E2\"$
\n" ); document.write( " $\"%28sqrt%286%29%29%5E2+=+%28-1+%2B+sqrt%282%29+%2B+2%29%5E2+%2B+%28-1+%2B+sqrt%282%29%29%5E2\"$
\n" ); document.write( " $\"6+=+1+%2B+2%2Asqrt%282%29+%2B+2+%2B+1+-+2%2Asqrt%282%29+%2B+2\"$
\n" ); document.write( " $\"6+=+6\"$
\n" ); document.write( "OK \n" ); document.write( "

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