Question

A rectangle has a perimeter of 80 inches. Write an equation to represent the area A in terms of width w.

Do I use the perimeter?

Answer 1

`A = 40w-w^2`

Explanation:

We are given the following in the question:

Perimeter of rectangle = 80 inches.

Let l be the length and w be the width of rectangle.

Perimeter of rectangle =

`P= 2(l+w)`

Putting values, we get,

`80 = 2(l+w)\\40 = l+w\\\Rightarrow l = 40 - w`

Now, we have to find the area of the rectangle in terms of w.

Area of rectangle =

`A = l* w`

Putting values, we get

`A = (40-w)w\\A = 40w-w^2`

is the required expression of area of rectangle in terms of w.

Yes, the perimeter is used to calculate the length of the rectangle in the term of w.