CRG6
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The area of a rectangle is 1 square inches. Express the perimeter P(w) as a function of the width w.

Respuesta :

Answer:

[tex]P(w)=2w+\frac{2}{w}[/tex]

Step-by-step explanation:

We are given the area of a rectangle is 1 inch square.

You can find the area of a rectangle if you know the dimensions. Let's pretend the dimensions are w and l.

So we given w*l=1.

Now the perimeter of a rectangle with dimensions l and w is 2w+2l.

We want to express P=2w+2l in terms of w only.

We are given that w*l=1 so l=1/w (just divided both sides of w*l=1 by w).

So let's plug it in for l (the 1/w thing).

[tex]P=2w+2(\frac{1}{w})[/tex]

So [tex]P(w)=2w+\frac{2}{w}[/tex].

alinakincsem

Answer:

P (w) = [tex]\frac{2}{w} +2w[/tex]

Step-by-step explanation:

We are given that the area of a rectangle is 1 square inches and we are to express the perimeter [tex]P(w)[/tex] as a function of the width [tex]w[/tex].

We know that:

Area of a rectangle = [tex]l \times w[/tex]

Substituting the given value of area in the above formula:

[tex]1=l \times w[/tex]

[tex]l=\frac{1}{w}[/tex]

Perimeter of a rectangle = [tex]2(l +w)[/tex]

Substituting the values in the formula to get:

Perimeter = [tex]2(\frac{1}{w}+w) =  \frac{2}{w} +2w[/tex]

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