document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200184>Question 1200184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design.<BR>\n" );
document.write( "Option 1: Side lengths: 4, 4, 8<BR>\n" );
document.write( "Option 2: Side lengths: 6, 8, 10<BR>\n" );
document.write( "Option 3: Side lengths: 6, 6, 13<BR>\n" );
document.write( "Part A. Which of the options would create a triangle for his design?<BR>\n" );
document.write( "Part B. The homeowner would like the porch to be in the shape of a right triangle. Will the carpenter be able to use any of the given options?<BR>\n" );
document.write( "Part C. For any option that does not form a triangle, what side length could be changed to<BR>\n" );
document.write( "form a triangle? Explain your answer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834375 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=834375\">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( "If a triangle has sides a,b,c then all of the following conditions must be true<BR>\n" );
document.write( "a < b+c<BR>\n" );
document.write( "b < a+c<BR>\n" );
document.write( "c < a+b<BR>\n" );
document.write( "Any two sides must add to be larger than the third side.<BR>\n" );
document.write( "See the <a  rel=nofollow HREF= \"https://www.mathsisfun.com/geometry/triangle-inequality-theorem.html\">triangle inequality theorem</a>.\r<BR>\n" );
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document.write( "In option 1, we have: a = 4, b = 4, c = 8<BR>\n" );
document.write( "And a+b = 4+4 = 8 which does not exceed c = 8<BR>\n" );
document.write( "In other words, c < a+b is not true.<BR>\n" );
document.write( "A triangle isn't possible here.<BR>\n" );
document.write( "Option 3 is a similar story.\r<BR>\n" );
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document.write( "Option 2 on the other hand works<BR>\n" );
document.write( "b+c = 8+10 = 18 exceeds a = 6 so a < b+c is true.<BR>\n" );
document.write( "a+c = 6+10 = 16 exceeds b = 8 so b < a+c is true.<BR>\n" );
document.write( "a+b = 6+8 = 14 exceeds c = 10 so c < a+b is true.<BR>\n" );
document.write( "A triangle is possible with sides 6, 8, and 10.\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "Use the pythagorean theorem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that a = 6, b = 8, c = 10 satisfy this equation. <BR>\n" );
document.write( "Therefore, option 2 represents a right triangle.\r<BR>\n" );
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document.write( "Part C\r<BR>\n" );
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document.write( "Let's look at option 1<BR>\n" );
document.write( "Let's say we knew the first two sides a = 4 and b = 4<BR>\n" );
document.write( "For a triangle to be possible, the third side c is given by this range <BR>\n" );
document.write( "b-a < c < b+a<BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%3E=+a ALIGN=MIDDLE  ALT=\"b+%3E=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See this my answer in this post for more info<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.1200226.html\">https://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.1200226.html</a>\r<BR>\n" );
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document.write( "The range for c in this case would be<BR>\n" );
document.write( "b-a < c < b+a<BR>\n" );
document.write( "4-4 < c < 4+4<BR>\n" );
document.write( "0 < c < 8\r<BR>\n" );
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document.write( "This means we could pick something like c = 5<BR>\n" );
document.write( "A triangle is possible with sides a = 4, b = 4, c = 5<BR>\n" );
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