document.write( "Question 203862: I would appreciate your help,
\n" ); document.write( "What are the sides of the rectangle with the largest area that can be inscribed in a right triangle whose sides are 6, 8 and 10 meter. \n" ); document.write( "
Algebra.Com's Answer #153983 by scott8148(6628)\"\" \"About 
You can put this solution on YOUR website!
picture the right-angle at the origin with the 6m side on the x-axis and the 8m side on the y-axis\r
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\n" ); document.write( "\n" ); document.write( "the corner of the rectangle opposite the origin lies on the hypotenuse at a point (x,y)
\n" ); document.write( "the equation of the hypotenuse is y = -4/3 x + 8\r
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\n" ); document.write( "\n" ); document.write( "the area of the rectangle is the product of the corner dimensions ___ A = x * y\r
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\n" ); document.write( "\n" ); document.write( "substituting ___ A = -4/3 x^2 + 8x\r
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\n" ); document.write( "\n" ); document.write( "the maximum value lies on the axis of symmetry of the quadratic
\n" ); document.write( "x = -b / 2a ___ x = -8 / (2 * -4/3) ___ x = 3\r
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\n" ); document.write( "\n" ); document.write( "substituting for y ___ y = -4/3 (3) + 8 = 4\r
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\n" ); document.write( "\n" ); document.write( "so the sides of the rectangle are 3m and 4m \n" ); document.write( "
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