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These 2 questions I need background/reasoning on every step of answer as I’ve never done this problem before.

These 2 questions I need background/reasoning on every step of answer as I’ve never-example-1

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Given:

The length of the rectangle ABCD (in metres)=


l=2x

Breadth of the rectangle ABCD (in metres)=


b=y

Perimeter of the rectangle ABCD (in metres)=


280\text{ }

Required:

(1) To show that the area A, of the rectangle can be written as:


A=280x-4x^2

(2) Maximum possible area that the rectangle can occupy.

Answer:

(1) We know that the perimeter(P) of the rectangle is,


P=2(l+b)

Therefore, substituting values, we get,


\begin{gathered} P=2(l+b) \\ 280=2(2x+y) \\ (280)/(2)=2x+y \\ 140=2x+y \\ y=140-2x \end{gathered}

Now, we know that the area(A) of the rectangle is,


A=l* b

Therefore, substituting values, we get,


\begin{gathered} A=l* b \\ A=2x* y \\ A=2x*(140-2x) \\ A=(2x*140)-(2x*2x) \\ A=280x-4x^2 \end{gathered}

Hence, the area A, of the rectangle can be written as:


A=280x-4x^2

(2) The maximum possible area that the rectangle can occupy is,


\begin{gathered} A=l* b \\ A=2x* y \\ A=2x*(140-2x) \\ A=(2x*140)-(2x*2x) \\ A=280x-4x^2 \end{gathered}

Hence, the maximum possible area of the rectangle is,


A=280x-4x^2

Final Answer:

The area A, of the rectangle can be written as:


A=280x-4x^2

The maximum possible area of the rectangle is,


A=280x-4x^2

User RallionRl
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