document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252312>Question 252312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a parallelogram with sides 12cm,8cm with one of the diagonal 10cm,find the length of other diagonal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184275 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> step 1: draw a parallelogram slanting right and label the base 12 and the slant height 8. <BR>\n" );
document.write( "step 2: draw a diagonal from top left to bottom right.<BR>\n" );
document.write( "step 3: construct an altitude from the top left vertex down to the base. call that \"h\".<BR>\n" );
document.write( "step 4: call the left side segment \"a\" and the right side segment \"b\". a + b = 12.<BR>\n" );
document.write( "step 5: we have 2 pythagorean theorems: (i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+h%5E2+=+8%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+h%5E2+=+8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; (ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+h%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+h%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "step 6: by subtracting the two, we get (iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+a%5E2+=+36 ALIGN=MIDDLE  ALT=\"b%5E2+-+a%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "step 7: find values for a and b such that (b+a)(b-a) = 36. If b= 9 and a = 3, we have the values.<BR>\n" );
document.write( "By using either (i) or (ii), this also gives us the height, h,  as sqrt(55).<BR>\n" );
document.write( "step 8: draw the other diagonal. Since we are dealing with a parallelogram, opposite sides have the same slope. So, the base grows from 12 to 15.<BR>\n" );
document.write( "step 9: we apply another pythagorean theorem to our new triangle. (iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2+%2B+sqrt%2855%29%5E2+=+d%5E2 ALIGN=MIDDLE  ALT=\"15%5E2+%2B+sqrt%2855%29%5E2+=+d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 10: solve for d. we get d^2 = 225 + 55 = 280. So, d ~ 16.7332.\r<BR>\n" );
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document.write( "Hope that helps.  </SPAN>\n" );
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