document.write( "Question 449981: The sum of the base and the height of a parallelogram is 24 in. Find the base and the height for which the area is a maximum. \n" ); document.write( "

Algebra.Com's Answer #309551 by Gogonati(855) $\"\"$ $\"About$

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Let the base of parallelogram x inches, then the height will be 24-x inches, and\r
\n" ); document.write( "\n" ); document.write( "the area is $\"A=x%2824-x%29=-x%5E2%2B24x=-%28x-12%29%5E2%2B144\"$ , which represent a downward \r
\n" ); document.write( "\n" ); document.write( "parabola with vertex (12, 144), and the maximum area is 144 square inches.\r
\n" ); document.write( "\n" ); document.write( "If you have knowledges about derivatives, find the maximum value of the function\r
\n" ); document.write( "\n" ); document.write( " $\"A=-x%5E2%2B24x\"$ . Its derivative is -2x+24, and the maximum value \r
\n" ); document.write( "\n" ); document.write( "will be: -2x+24=0 for x=12.\r
\n" ); document.write( "\n" ); document.write( "Answer:The maximum area of the parallelogram will be, where the base and height are equal with 12 inches. \n" ); document.write( "

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