document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136404>Question 1136404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given: <BR>\n" );
document.write( "MK⊥LM, MK⊥KN<BR>\n" );
document.write( "MN=13, KL=15, LM-KN=4 <BR>\n" );
document.write( "Find:    Area of KLMN.\r<BR>\n" );
document.write( "\n" );
document.write( "https://lh3.googleusercontent.com/5QOz1XKjH41wSp7YLvf8CQHlJJmXpmR_TCV_t5zhia7mfJma9ozdGPlwiSOVYHE753-V3Q=s170 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754172 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13216)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Since all the measurements are whole numbers, we can easily solve the problem by guessing, knowing that the side lengths of right triangles KMN and KML are Pythagorean triples.<br><BR>\n" );
document.write( "Since MN=13, KN is almost certainly either 5 or 12.  Trying KN=5 makes MK=12 and LM=9; and that makes triangle KML a Pythagorean triple 9, 12, and 15.<br><BR>\n" );
document.write( "So triangle KMN is a 5-12-13 triangle with area (5*12)/2 = 30; triangle KML is a 9-12-15 triangle with area (9*12)/2 = 54.<br><BR>\n" );
document.write( "Then the area of KLMN is 30+54 = 84.<br><BR>\n" );
document.write( "The problem can be solved formally using the Pythagorean Theorem.<br><BR>\n" );
document.write( "Let KN = x; then LM = x+4.  And let KM = y.  Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2+=+13%5E2+=+169 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2+=+13%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2By%5E2+=+x%5E2%2B8x%2B16%2By%5E2+=+225 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2By%5E2+=+x%5E2%2B8x%2B16%2By%5E2+=+225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B16+=+56 ALIGN=MIDDLE  ALT=\"8x%2B16+=+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+=+40 ALIGN=MIDDLE  ALT=\"8x+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the rest of the path to the answer to the question is the same as above. </SPAN>\n" );
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