document.write( "Question 287984: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures rr 6 meters. find the width and height. \n" ); document.write( "

Algebra.Com's Answer #208685 by stanbon(75887) $\"\"$ $\"About$

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The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures rr 6 meters. find the width and height.
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\n" ); document.write( "Let height be x meters
\n" ); document.write( "Then width is \"x+2\" meters.
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\n" ); document.write( "Use Pythagoras to find width and height:
\n" ); document.write( "Equation:
\n" ); document.write( "x^2 + (x+2)^2 = 6^2
\n" ); document.write( "x^2 + x^2 + 4x + 4 = 36
\n" ); document.write( "2x^2 + 4x - 32 = 0
\n" ); document.write( "x^2 + 2x - 16 = 0
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\n" ); document.write( "x = [-2 +- sqrt(4 - 4*-16)]/2
\n" ); document.write( "---
\n" ); document.write( "x = [-2 +- sqrt(68)]/2
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\n" ); document.write( "x = [-2 +- 2sqrt(17)]/2
\n" ); document.write( "---
\n" ); document.write( "x = [-1 +-sqrt(17)]
\n" ); document.write( "---
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = -1+sqrt(17) is appoximately 3.1231m (width)
\n" ); document.write( "---
\n" ); document.write( "x+2 = 5.1231m (length)
\n" ); document.write( "===========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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