document.write( "Question 146024: The width of a rectangular gate is 2 meters larger than its height. The diagonal brace measures square root of 6 meters. Find the width and height. \n" ); document.write( "

Algebra.Com's Answer #106573 by nerdybill(7384) $\"\"$ $\"About$

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Draw a diagram -- label what you know. You'll see that the length, width and diagonal forms a right triangle. If so, then you can apply Pythagorean theorem:
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\n" ); document.write( "Let h = height
\n" ); document.write( "then h+2 = width
\n" ); document.write( "from Pythagorean we have
\n" ); document.write( "h^2 + (h+2)^2 = 6
\n" ); document.write( "h^2 + h^2 + 4h + 4 = 6
\n" ); document.write( "2h^2 + 4h + 4 = 6
\n" ); document.write( "2h^2 + 4h - 2 = 0
\n" ); document.write( "divide both sides by 2:
\n" ); document.write( "h^2 + 2h - 1 = 0
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\n" ); document.write( "Since we can't factor, you must use the quadratic equation which will yield:
\n" ); document.write( "h = 0.414 meters (height)
\n" ); document.write( "h+2 = 2.414 meters (width)
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