document.write( "Question 1193656: Find the area of a triangle bounded by the y axis, the line f(x)=5-1/5x, and the line perpendicular to f(x) that passes through the origin
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Algebra.Com's Answer #825696 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The line f(x) = 5 -   has x-intercept at  \r\n" );
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document.write( "    5 -  = 0  ---->  25 - x = 0  ---->  x = 25.\r\n" );
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document.write( "So, the hypotenuse of the triangle lies on x-axis and goes from the origin to x= 25,\r\n" );
document.write( "having the length of 25 units.\r\n" );
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document.write( "The perpendicular line is  y = 5x  (from analysis of slopes).\r\n" );
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document.write( "The intersection point of these two lines  (x-coordinate) can be found as the solution to this equation\r\n" );
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document.write( "    5 -  = 5x.\r\n" );
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document.write( "Simplifying, we get\r\n" );
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document.write( "    25 - x = 25x\r\n" );
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document.write( "    25 = 25x + x \r\n" );
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document.write( "    25 = 26x  ---->  x = .\r\n" );
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document.write( "Then y-coordinate of the intercetion point is  y = 5x =  =.\r\n" );
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document.write( "Now the area of the triangle is half the product of its hypotenuse, which is 25 units,\r\n" );
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document.write( "by , which is y-coordinate of the intersection point, i.e. its distance from x-axis.\r\n" );
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document.write( "Therefore,  the area of the triangle is  \r\n" );
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document.write( "    area =  =  = 60 = 60.096 square units (rounded).    ANSWER\r\n" );
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