document.write( "Question 797968: If one side of an equilateral triangle is along the line 12x+5y-26=0 and the opposite vertex is on the line 12x+5y+13=0, what is its area? \n" ); document.write( "
Algebra.Com's Answer #481985 by josgarithmetic(39625)\"\" \"About 
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A triangle does not have any opposite vertices. Your description needs more information to restrict the third line in order to find an area. \r
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\n" ); document.write( "\n" ); document.write( "You have two parallel lines. You can find the distance between these two lines, and this distance will be the altitude or height of an equilateral triangle. \r
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\n" ); document.write( "\n" ); document.write( "\"12x%2B5y=26\"
\n" ); document.write( "\"5y=-12x%2B26\"
\n" ); document.write( "\"y=-%2812%2F5%29x%2B26%2F5\" is one line, and
\n" ); document.write( "\"y=-%2812%2F5%29x-13%2F5\" is the other line.\r
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\n" ); document.write( "\n" ); document.write( "ANY segment perpendicular to these lines, and with endpoints on these lines will serve. Let's pick point, (0,26/5) and some line of slope \"5%2F12\". What is the line of slope \"5%2F12\" and containing point (0,26/5)?\r
\n" ); document.write( "\n" ); document.write( "\"y=%285%2F12%29x%2Bb\" where y-intercept is b.
\n" ); document.write( "\"b=y-%285%2F12%29x\"
\n" ); document.write( "\"b=26%2F5-%285%2F12%29%2A0\"
\n" ); document.write( "\"b=26%2F5\", but we already knew this by how we picked it.\r
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\n" ); document.write( "\n" ); document.write( "The line \"y=%285%2F12%29x%2B26%2F5\" is perpendicular to the two given parallel lines.
\n" ); document.write( "WHAT POINT is the intersection of \"y=%285%2F12%29x%2B26%2F5\" and \"y=-%2812%2F5%29x-13%2F5\" ?
\n" ); document.write( "\"%285%2F12%29x%2B26%2F5=-%2812%2F5%29x-13%2F5\"
\n" ); document.write( "Multiply both sides by 60,
\n" ); document.write( "\"25x%2B26%2A12=-144-13%2A12\"
\n" ); document.write( "\"25x=-26%2A12-12%2A12-13%2A12\"
\n" ); document.write( "\"25x=-12%2826%2B12%2B13%29=-12%2A51\"
\n" ); document.write( "\"x=-12%2A51%2F25\"
\n" ); document.write( "\"x=-612%2F25\"
\n" ); document.write( "Find the y value: \"y=%285%2F12%29%28-612%2F25%29%2B26%2F5\"
\n" ); document.write( "\"y=-%285%2A612%29%2F%2812%2A25%29%2B%2826%2F5%29%28%285%2A12%29%2F%285%2A12%29%29\"
\n" ); document.write( "\"y=-5\" after all the computation and simplification.\r
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\n" ); document.write( "\n" ); document.write( "We then want to use the Distance Formula to find length from (-612/25,-5) and (0,26/5). THAT WILL BE THE HEIGHT OF THE EQUILATERAL TRIANGLE. \r
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\n" ); document.write( "\n" ); document.write( "Knowing this height, h, you can find the base of the triangle. Can you finish this?
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