document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187206>Question 1187206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the dimension of rectangular metal box are 3cm 5cm and 8 cm. if the first 2 dimension are increased by the same numbers of centimeters, while the 3rd dimension remains the same, the new volume is 34cmcube more than the original volume. what is the new dimension of the enlarged rectangular metal box?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818150 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = amount we increase the first two dimensions by<BR>\n" );
document.write( "The x is a placeholder for some positive number<BR>\n" );
document.write( "The old box is 3 by 5 by 8<BR>\n" );
document.write( "The new box is (3+x) by (5+x) by 8\r<BR>\n" );
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document.write( "The old volume was<BR>\n" );
document.write( "V1 = 3*5*8 = 120 cm^3\r<BR>\n" );
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document.write( "The new volume is<BR>\n" );
document.write( "V2 = (3+x)*(5+x)*8<BR>\n" );
document.write( "V2 = (15+3x+5x+x^2)*8<BR>\n" );
document.write( "V2 = 8(x^2+8x+15)<BR>\n" );
document.write( "V2 = 8x^2+64x+120\r<BR>\n" );
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document.write( "This new volume (V2) is 34 cm^3 larger compared to the old volume (V1)\r<BR>\n" );
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document.write( "V2 = V1 + 34<BR>\n" );
document.write( "8x^2+64x+120 = 120 + 34<BR>\n" );
document.write( "8x^2+64x+120 = 154<BR>\n" );
document.write( "8x^2+64x+120-154 = 0<BR>\n" );
document.write( "8x^2+64x-34 = 0<BR>\n" );
document.write( "2(4x^2+32x-17) = 0<BR>\n" );
document.write( "4x^2+32x-17 = 0\r<BR>\n" );
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document.write( "Use factoring or the quadratic formula to find the two possible solutions are:<BR>\n" );
document.write( "x = -17/2 or x = 1/2<BR>\n" );
document.write( "Ignore the first solution. Negative lengths are not possible.\r<BR>\n" );
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document.write( "The only practical solution is that we increased the first two dimensions by 1/2 = 0.5 cm\r<BR>\n" );
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document.write( "The first two dimensions of 3 cm and 5 cm become 3.5 cm and 5.5 cm\r<BR>\n" );
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document.write( "Old Box = 3 cm by 5 cm by 8 cm<BR>\n" );
document.write( "New Box = 3.5 cm by 5.5 cm by 8 cm<BR>\n" );
document.write( "Old volume = 3*5*8 = 120<BR>\n" );
document.write( "New volume = 3.5*5.5*8 = 154<BR>\n" );
document.write( "Difference in volumes = 154-120 = 34<BR>\n" );
document.write( "The answer is confirmed.\r<BR>\n" );
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document.write( "Answer: <font color=red>3.5 cm by 5.5 cm by 8 cm</font><BR>\n" );
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