document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196783>Question 1196783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sides of a parallelogram ABCD are AB= 424mm and AD= 348mm<BR>\n" );
document.write( "If angle ABC is 130°\r<BR>\n" );
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document.write( "a. Find the lengths of long and short diagonals.<BR>\n" );
document.write( "b. Find the area of and perimeter of a parallelogram </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829775 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=829775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "Diagram:<BR>\n" );
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document.write( "Draw a segment from A to C. This is the longer diagonal.\r<BR>\n" );
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document.write( "Focus on triangle ABC<BR>\n" );
document.write( "Side 'a' is opposite angle A<BR>\n" );
document.write( "Side 'b' is opposite angle B<BR>\n" );
document.write( "Side 'c' is opposite angle C\r<BR>\n" );
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document.write( "For triangle ABC, we have<BR>\n" );
document.write( "a = 348<BR>\n" );
document.write( "b = unknown<BR>\n" );
document.write( "c = 424<BR>\n" );
document.write( "angle B = 130 degrees\r<BR>\n" );
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document.write( "Apply the law of cosines.<BR>\n" );
document.write( "Make sure your calculator is in degree mode.<BR>\n" );
document.write( "b^2 = a^2+c^2 - 2*a*c*cos(B)<BR>\n" );
document.write( "b^2 = 348^2+424^2 - 2*348*424*cos(130)<BR>\n" );
document.write( "b^2 = 490,569.194768937<BR>\n" );
document.write( "b = sqrt(490,569.194768937)<BR>\n" );
document.write( "b = 700.406449691132<BR>\n" );
document.write( "<font color=red>The longer diagonal (AC) is approximately 700.406 mm long</font>\r<BR>\n" );
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document.write( "Return to the original parallelogram diagram shown at the top. Draw a line from B to D to form triangle ABD\r<BR>\n" );
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document.write( "Angle DAB is 180-(angleABC) = 180-130 = 50 degrees<BR>\n" );
document.write( "This is angle A of triangle ABD\r<BR>\n" );
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document.write( "We have this info about triangle ABD<BR>\n" );
document.write( "side b = 348<BR>\n" );
document.write( "side d = 424<BR>\n" );
document.write( "angle A = 50 degrees\r<BR>\n" );
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document.write( "Use the law of cosines<BR>\n" );
document.write( "a^2 = b^2+d^2 - 2*b*d*cos(A)<BR>\n" );
document.write( "a^2 = 348^2+424^2 - 2*348*424*cos(50)<BR>\n" );
document.write( "a^2 = 111,190.805231063<BR>\n" );
document.write( "a = sqrt(111,190.805231063)<BR>\n" );
document.write( "a = 333.452853085802<BR>\n" );
document.write( "<font color=red>The shorter diagonal (BD) is approximately 333.453 mm long</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "AB = CD = 424<BR>\n" );
document.write( "AD = BC = 348\r<BR>\n" );
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document.write( "Area = side1*side2*sin(included angle)<BR>\n" );
document.write( "Area = AB*BC*sin(angle ABC)<BR>\n" );
document.write( "Area = 424*348*sin(130)<BR>\n" );
document.write( "<font color=red>Area = 113,031.389671091 square mm approximately</font>\r<BR>\n" );
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document.write( "Perimeter = AB+BC+CD+AD<BR>\n" );
document.write( "Perimeter = AB+AD+AB+AD<BR>\n" );
document.write( "Perimeter = 2*AB + 2*AD<BR>\n" );
document.write( "Perimeter = 2*(AB + AD)<BR>\n" );
document.write( "Perimeter = 2*(424 + 348)<BR>\n" );
document.write( "Perimeter = 2*(772)<BR>\n" );
document.write( "<font color=red>Perimeter = 1544 mm</font><BR>\n" );
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