document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186910>Question 1186910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Treena just graduated Med School. How exciting! Her parents wanted to give her a gift to celebrate. They<BR>\n" );
document.write( "wanted to frame her diploma from the University of Toronto. The diploma itself is 10 inches by 12 inches.<BR>\n" );
document.write( "They thought that a border of equal width makes sense to do. They wanted the area of the border to be<BR>\n" );
document.write( "exactly equal to 25% of the area of the diploma. What length should the width of the border be? What would<BR>\n" );
document.write( "be the dimensions of the framed diploma? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849331 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem:\r<BR>\n" );
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document.write( "**1. Area of the diploma:**\r<BR>\n" );
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document.write( "The diploma is 10 inches by 12 inches, so its area is 10 * 12 = 120 square inches.\r<BR>\n" );
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document.write( "**2. Area of the border:**\r<BR>\n" );
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document.write( "The border's area is 25% of the diploma's area, so it's 0.25 * 120 = 30 square inches.\r<BR>\n" );
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document.write( "**3. Dimensions of the framed diploma:**\r<BR>\n" );
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document.write( "Let 'x' be the width of the border.  The framed diploma will have dimensions (10 + 2x) inches by (12 + 2x) inches.\r<BR>\n" );
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document.write( "**4. Area of the framed diploma:**\r<BR>\n" );
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document.write( "The area of the framed diploma is (10 + 2x)(12 + 2x).\r<BR>\n" );
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document.write( "**5. Set up the equation:**\r<BR>\n" );
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document.write( "The area of the framed diploma is equal to the area of the diploma plus the area of the border:\r<BR>\n" );
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document.write( "(10 + 2x)(12 + 2x) = 120 + 30<BR>\n" );
document.write( "(10 + 2x)(12 + 2x) = 150\r<BR>\n" );
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document.write( "**6. Expand and simplify the equation:**\r<BR>\n" );
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document.write( "120 + 20x + 24x + 4x² = 150<BR>\n" );
document.write( "4x² + 44x + 120 = 150<BR>\n" );
document.write( "4x² + 44x - 30 = 0<BR>\n" );
document.write( "2x² + 22x - 15 = 0\r<BR>\n" );
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document.write( "**7. Solve for x using the quadratic formula:**\r<BR>\n" );
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document.write( "x = (-b ± √(b² - 4ac)) / 2a<BR>\n" );
document.write( "x = (-22 ± √(22² - 4 * 2 * -15)) / (2 * 2)<BR>\n" );
document.write( "x = (-22 ± √(484 + 120)) / 4<BR>\n" );
document.write( "x = (-22 ± √604) / 4<BR>\n" );
document.write( "x = (-22 ± 2√151) / 4<BR>\n" );
document.write( "x = (-11 ± √151) / 2\r<BR>\n" );
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document.write( "Since x represents a width, it must be positive.  Therefore:\r<BR>\n" );
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document.write( "x = (-11 + √151) / 2<BR>\n" );
document.write( "x ≈ (-11 + 12.288) / 2<BR>\n" );
document.write( "x ≈ 1.288 / 2<BR>\n" );
document.write( "x ≈ 0.644 inches\r<BR>\n" );
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document.write( "**8. Dimensions of the framed diploma:**\r<BR>\n" );
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document.write( "*   Width: 10 + 2x ≈ 10 + 2 * 0.644 ≈ 11.288 inches<BR>\n" );
document.write( "*   Height: 12 + 2x ≈ 12 + 2 * 0.644 ≈ 13.288 inches\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "The width of the border should be approximately 0.644 inches. The dimensions of the framed diploma would be approximately 11.29 inches by 13.29 inches.<BR>\n" );
document.write( " </SPAN>\n" );
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