document.write( "Question 825635: The perimeter of a rectangle is 64 cm.\r
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document.write( "A) Obtain an equation the represents the area of the rectangle in terms of its length. [Hint: Recall that the area of a rectangle is A=LxW and the perimeter is P=2(L+W)].\r
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document.write( "B) Determine the length and the width that give the maximum area.\r
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document.write( "C) Determine the maximum possible area of the rectangle?\r
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document.write( "Please help me I don't understand this question. Thank you \n" );
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Algebra.Com's Answer #497460 by TimothyLamb(4379)![]() ![]() You can put this solution on YOUR website! --- \n" ); document.write( "x = length \n" ); document.write( "y = width \n" ); document.write( "--- \n" ); document.write( "64 = 2x + 2y \n" ); document.write( "a = xy \n" ); document.write( "--- \n" ); document.write( "NOTE TO STUDENT: \n" ); document.write( "explanation of the above equations: \n" ); document.write( "--- \n" ); document.write( "this equation: 64 = 2x + 2y \n" ); document.write( "is for the perimeter of the given rectangle. \n" ); document.write( "we are told that the rectangle perimeter = 64 cm \n" ); document.write( "--- \n" ); document.write( "perimeter is just the sum of all the sides of a rectangle. \n" ); document.write( "two sides measure x each, so 2x \n" ); document.write( "the other two sides measure y each, so 2y \n" ); document.write( "so the sum of all four sides is: 2x + 2y \n" ); document.write( "--- \n" ); document.write( "this equation: a = xy \n" ); document.write( "is for the area of a generic rectangle. \n" ); document.write( "by definition, the area of a rectangle is the product of its length (x) and its width (y), so xy \n" ); document.write( "\"a\" is just a symbol (variable) representing area \n" ); document.write( "--- \n" ); document.write( "now solve for y (width) in terms of x (length): \n" ); document.write( "64 = 2x + 2y \n" ); document.write( "2y = 64 - 2x \n" ); document.write( "y = (64 - 2x)/2 \n" ); document.write( "y = 32 - x \n" ); document.write( "--- \n" ); document.write( "now substitute for y in the area equation, to get area in terms of x (length) only: \n" ); document.write( "a = xy \n" ); document.write( "a = x(32 - x) \n" ); document.write( "a = 32x - xx \n" ); document.write( "--- \n" ); document.write( "answer A: \n" ); document.write( "a = -xx + 32x \n" ); document.write( "--- \n" ); document.write( "the above quadratic equation is in standard form, with a=-1, b=32, and c=0 \n" ); document.write( "--- \n" ); document.write( "to solve the quadratic equation, by using the quadratic formula, copy and paste this: \n" ); document.write( "-1 32 0 \n" ); document.write( "into this solver: https://sooeet.com/math/quadratic-equation-solver.php \n" ); document.write( "--- \n" ); document.write( "the quadratic vertex is a maximum at: ( x= 16, a= 256 ) \n" ); document.write( "--- \n" ); document.write( "the maximum area of the rectangle (256 sq.cm) occurs when x (length) = 16 cm \n" ); document.write( "a = xy \n" ); document.write( "256 = xy \n" ); document.write( "y = 256/x \n" ); document.write( "y = 256/16 \n" ); document.write( "y = 16 \n" ); document.write( "--- \n" ); document.write( "answer B: \n" ); document.write( "rectangle dimensions for maximum area: \n" ); document.write( "x = length = 16 cm \n" ); document.write( "y = width = 16 cm \n" ); document.write( "--- \n" ); document.write( "answer C: \n" ); document.write( "the maximum area of the rectangle = 256 sq.cm \n" ); document.write( "--- \n" ); document.write( "Solve and graph linear equations: \n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php \n" ); document.write( "--- \n" ); document.write( "Solve quadratic equations, quadratic formula: \n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php \n" ); document.write( "--- \n" ); document.write( "Solve systems of linear equations up to 4-equations 4-variables: \n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php \n" ); document.write( " |