document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896764>Question 896764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of an isosceles triangle is 600 square meter. Each equal side is 13 m. Find the length of the base .\r<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 #543744 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=543744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 600 square doesn't sound right.\r<BR>\n" );
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document.write( "there's no way you can have that.\r<BR>\n" );
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document.write( "let me explain.\r<BR>\n" );
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document.write( "a right triangle with a hypotenuse of 13 units will have legs of 5 and 12.\r<BR>\n" );
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document.write( "this is because 5^2 + 12^2 = 13^2\r<BR>\n" );
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document.write( "your isosceles triangle is composed of two right triangle back to back.\r<BR>\n" );
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document.write( "the area of each of the right triangles will be 1/2 * 5 * 12 = 1/2 * 60 = 30\r<BR>\n" );
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document.write( "multiply that by 2 and you get an area of 60 square units.\r<BR>\n" );
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document.write( "if the area of the isosceles triangle is 60 square units, then the problem can be solved.\r<BR>\n" );
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document.write( "if it's not, then the problem can't be solved.\r<BR>\n" );
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document.write( "assuming the area is 60 square units rather than 600, I would solve as follows:\r<BR>\n" );
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document.write( "area of the isosceles triangle is equal to 2 times the area of the right triangle that is formed when you drop an altitude from the vertex to the base.\r<BR>\n" );
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document.write( "each of these right triangles has 13 as a hypotgenuse.   these are the equal legs of the isosceles triangle.\r<BR>\n" );
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document.write( "the area of each of these right triangles is equal to 1/2 * b * h which is equal to 30 square units.\r<BR>\n" );
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document.write( "so for each of the right triangles, the formula for the area becomes:\r<BR>\n" );
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document.write( "A = 1/2 * b * h which becomes:\r<BR>\n" );
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document.write( "30 = 1/2 * b * h\r<BR>\n" );
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document.write( "we don't know b or h, but we do know that:\r<BR>\n" );
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document.write( "b^2 + h^2 = 13^2\r<BR>\n" );
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document.write( "we solve for h in terms of b as follows:\r<BR>\n" );
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document.write( "b^2 + h^2 = 13^2\r<BR>\n" );
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document.write( "subtract b^2 from both sides of the equation to get:\r<BR>\n" );
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document.write( "h^2 = (13^2 - b^2)\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "h = square root of (13^2 - b^2)\r<BR>\n" );
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document.write( "formula for  the area of a right triangle now becomes:\r<BR>\n" );
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document.write( "30 = 1/2 * b * h which becomes:\r<BR>\n" );
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document.write( "30 = 1/2 * b * sqrt(13^2 - b^2)\r<BR>\n" );
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document.write( "we can now solve for b as follows:\r<BR>\n" );
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document.write( "multiply both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "60 = b * sqrt(13^2 - b^2)\r<BR>\n" );
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document.write( "square both sides of this equation to get:\r<BR>\n" );
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document.write( "3600 = b^2 * (13^2 - b^2)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3600 = b^2 * 169 - b^2 * b^2 which becomes:\r<BR>\n" );
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document.write( "3600 = 169*b^2 - b^4\r<BR>\n" );
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document.write( "add b^4 to both sides of this equation and subtract 169b^2 from both sides of this equation to get:\r<BR>\n" );
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document.write( "b^4 - 169b^2 + 3600 = 0\r<BR>\n" );
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document.write( "let x = b^2 and the equation becomes:\r<BR>\n" );
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document.write( "x^2 - 169x + 3600 = 0\r<BR>\n" );
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document.write( "factor this equation to get:\r<BR>\n" );
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document.write( "(x-25) * (x-144) = 0\r<BR>\n" );
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document.write( "solve for x to get;\r<BR>\n" );
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document.write( "x = 25 or x = 144\r<BR>\n" );
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document.write( "now replace x with b^2 and you get:\r<BR>\n" );
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document.write( "b^2 = 25 or b^2 = 144\r<BR>\n" );
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document.write( "solve for b to get:\r<BR>\n" );
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document.write( "b = 5 or b = 12\r<BR>\n" );
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document.write( "now that you know b, you can solve for h.\r<BR>\n" );
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document.write( "when b = 5, h = 12\r<BR>\n" );
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document.write( "when b = 12, h = 5\r<BR>\n" );
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document.write( "in both cases, the area of the right triangle is 1/2 * b * h = 1/2 * 5 * 12 = 1/2 * 60 = 30\r<BR>\n" );
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document.write( "the 2 right triangles make up the isosceles triangle and the area of the isosceles triangle is 60.\r<BR>\n" );
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document.write( "the length of the base of the isosceles triangle is 2 times the length of the base of each right triangle.\r<BR>\n" );
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document.write( "the base will therefore be either 24 or 10, depending on whether the height of the isosceles triangle is 5 or 12.\r<BR>\n" );
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document.write( "the following picture should show you what i mean.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/090105.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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