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