document.write( "Question 789258: The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 81 \"cm\"^2, what is the length of the diagonal? \n" ); document.write( "

Algebra.Com's Answer #478799 by waynest(281) $\"\"$ $\"About$

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w = 2L - 6
\n" ); document.write( "A = Lw
\n" ); document.write( "81 = L(2L -6)
\n" ); document.write( "81 = 2L^2 -6L
\n" ); document.write( "81 - 81 = 2L^2 - 6L - 81
\n" ); document.write( "0 = 2L^2 -6L - 81
\n" ); document.write( "use quadratic formula\r
\n" ); document.write( "\n" ); document.write( "(-b +-sqrtb^2 - 4(a)(c))/2(a) a = 2, b = -6, c = -81
\n" ); document.write( "(-(-6) +-sqrt-6^2 - 4(2)9-81))/2(2)
\n" ); document.write( "(6 +-sqrt16 + 648)/4
\n" ); document.write( "(6 +-sqrt684)/4
\n" ); document.write( "(6 +- 6sqrt19)/4
\n" ); document.write( "x =(6 +- 6sqrt19)/4
\n" ); document.write( "x = (3 +-3sqrt19)/2\r
\n" ); document.write( "\n" ); document.write( "x = (3 + 3sqrt19)/2
\n" ); document.write( "x = 8.038\r
\n" ); document.write( "\n" ); document.write( "x = (3 - 3sqrt19)/2
\n" ); document.write( "x = -5.038
\n" ); document.write( "you can't have a negative value so use 8.038\r
\n" ); document.write( "\n" ); document.write( "c^2 = a^2 + b^2 a = 8.038, b = 2(8.038) - 6 = 10.077
\n" ); document.write( "c^2 = 8.038^2 + 10.077^2
\n" ); document.write( "c^2 = 166.155
\n" ); document.write( "sqrtc^2 = sqrt166.155
\n" ); document.write( "c = 12.890
\n" ); document.write( "the diagonal is 12.890 cm \n" ); document.write( "

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