Question

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

Answer 1

`P(w)=2w+(2)/(w)`

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((1)/(w))`

So
`P(w)=2w+(2)/(w)`.

Answer 2

P (w) =
`(2)/(w) +2w`

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 * w`

Substituting the given value of area in the above formula:

`1=l * w`

`l=(1)/(w)`

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

Substituting the values in the formula to get:

Perimeter =
`2((1)/(w)+w) =  (2)/(w) +2w`