document.write( "Question 1200298: Let the width(w) and the area(A) be real numbers. The perimeter remains a constant 24cm. Draw a graph for 1<=w<=11 that represents the relationship between the width and the area. Label the axes appropriately \n" ); document.write( "

Algebra.Com's Answer #834399 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "x = width
\n" ); document.write( "P = perimeter
\n" ); document.write( "P = 2*length + 2*width
\n" ); document.write( "24 = 2*length + 2*width
\n" ); document.write( "12 = length + width
\n" ); document.write( "12 = length + x
\n" ); document.write( "length = 12-x\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A(x) = area
\n" ); document.write( "A(x) = length*width
\n" ); document.write( "A(x) = (12-x)*x
\n" ); document.write( "A(x) = -x^2+12x\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Graph of A(x) when 1 <= x <= 11
\n" ); document.write( "

\n" ); document.write( "x = width
\n" ); document.write( "A(x) = area of the rectangle\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Table of selected values
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

x	A(x)
1	11
2	20
3	27
4	32
5	35
6	36
7	35
8	32
9	27
10	20
11	11

\n" ); document.write( "(6,36) is the vertex since it's the highest point.
\n" ); document.write( "This vertex point tells us that the area is maxed out at 36 square cm when the width is x = 6 cm.
\n" ); document.write( " \n" ); document.write( "

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