document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200779>Question 1200779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. If one of the legs of a right triangle is three times the other and the perimeter of the triangle is 45m,find its area.<BR>\n" );
document.write( "2. The area of a triangle is 65m^2 and the triangle is an equiangular triangle. Find the length of the three sides.<BR>\n" );
document.write( "3. The area of a triangle is 8346m^2 and two of its interior angles are 37°25' and 56°17'. What is the length of the longest side?.<BR>\n" );
document.write( "4. In a triangle ABC; AC= 60cm, BC= 30cm, and angle B=80°30',Find side AB. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835013 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=835013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You are allowed only one question per post. <BR>\n" );
document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
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document.write( "x = some positive number, i.e. x > 0<BR>\n" );
document.write( "a = x = smaller leg<BR>\n" );
document.write( "b = 3x = larger leg<BR>\n" );
document.write( "c = unknown hypotenuse\r<BR>\n" );
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document.write( "Use the Pythagorean Theorem to determine what c is in terms of x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28x%5E2%2B%283x%29%5E2%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%28x%5E2%2B%283x%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%2810%29%2Asqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"c+=+sqrt%2810%29%2Asqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%2810%29%2Ax ALIGN=MIDDLE  ALT=\"c+=+sqrt%2810%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Note that x > 0 so sqrt(x^2) = x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+x%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"c+=+x%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add up the three sides of the triangle. Set the sum equal to the stated perimeter 45. Solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc+=+perimeter ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc+=+perimeter\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3x%2Bx%2Asqrt%2810%29+=+45 ALIGN=MIDDLE  ALT=\"x%2B3x%2Bx%2Asqrt%2810%29+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2Bx%2Asqrt%2810%29+=+45 ALIGN=MIDDLE  ALT=\"4x%2Bx%2Asqrt%2810%29+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Bsqrt%2810%29%29x+=+45 ALIGN=MIDDLE  ALT=\"%284%2Bsqrt%2810%29%29x+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+45%2F%284%2Bsqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"x+=+45%2F%284%2Bsqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's rationalize the denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28180-45sqrt%2810%29%29%2F%28%284%29%5E2-%28sqrt%2810%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"x+=+%28180-45sqrt%2810%29%29%2F%28%284%29%5E2-%28sqrt%2810%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2860-15%2Asqrt%2810%29%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2860-15%2Asqrt%2810%29%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2860-15%2Asqrt%2810%29%29%29%2F%283%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2860-15%2Asqrt%2810%29%29%29%2F%283%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2860-15%2Asqrt%2810%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2860-15%2Asqrt%2810%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because each leg of the right triangle is perpendicular to one another, we can treat them as the base and height in either order.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area+=+%281%2F2%29%2Abase%2Aheight ALIGN=MIDDLE  ALT=\"area+=+%281%2F2%29%2Abase%2Aheight\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in the expression we found for x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area+=+%283%2F2%29%28%2860-15%2Asqrt%2810%29%29%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"area+=+%283%2F2%29%28%2860-15%2Asqrt%2810%29%29%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area+=+%283%2F2%29%28%28%2860-15%2Asqrt%2810%29%29%5E2%29%2F4%29 ALIGN=MIDDLE  ALT=\"area+=+%283%2F2%29%28%28%2860-15%2Asqrt%2810%29%29%5E2%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area+=+%283%2F8%29%2860-15%2Asqrt%2810%29%29%5E2 ALIGN=MIDDLE  ALT=\"area+=+%283%2F8%29%2860-15%2Asqrt%2810%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area+=+%283%2F8%29%2860%5E2-2%2A60%2A15%2Asqrt%2810%29%2B%2815%2Asqrt%2810%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"area+=+%283%2F8%29%2860%5E2-2%2A60%2A15%2Asqrt%2810%29%2B%2815%2Asqrt%2810%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the formula (m+n)^2 = m^2+2mn+n^2\r<BR>\n" );
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document.write( "When using a calculator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288775-2700%2Asqrt%2810%29%29%2F4+=+59.21258 ALIGN=MIDDLE  ALT=\"%288775-2700%2Asqrt%2810%29%29%2F4+=+59.21258\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximate to five decimal places.<BR>\n" );
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