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A rectangle has sides of lengths x and 2x. How do you express the area A of the rectangle as a function of it perimeter P?

Answer 1

Eva Adamson

The area #A# of the rectangle as a function of it perimeter #P# is #P^2/18#.

As the sides of rectangle are #x# and #2x#, its perimeter #P# is given by #P=2×(x+2x)=6x#.

or #x=1/6P=P/6#

Area of rectangle #A# is #x×2x=2x^2=2×(P/6)^2=2×P^2/36=P^2/18#.

Hence the area #A# of the rectangle as a function of it perimeter #P# is #P^2/18#.

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Answer 2

Jameson Allen

The area ( A ) of the rectangle can be expressed as a function of its perimeter ( P ) using the following equation:

[ A(x) = \frac{P(x)}{2} - x^2 ]

Where ( P(x) ) represents the perimeter of the rectangle, and ( x ) represents the length of one of its sides.

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Answer from HIX Tutor

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