Question

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

Answer 1

Answer:

P (w) = $\frac{2}{w} +2w$

Step-by-step explanation:

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

We know that:

Area of a rectangle = $l \times w$

Substituting the given value of area in the above formula:

$1=l \times w$

$l=\frac{1}{w}$

Perimeter of a rectangle = $2(l +w)$

Substituting the values in the formula to get:

Perimeter = $2(\frac{1}{w}+w) = \frac{2}{w} +2w$

Answer 2

Answer:

$P(w)=2w+\frac{2}{w}$

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).

$P=2w+2(\frac{1}{w})$

So $P(w)=2w+\frac{2}{w}$.