Question

You have 30 feet of wire fencing that you want to use to make a rectangular pen for chickens. Let l be the length of the pen. what is a polynomial expression in terms of l for the area of the pen?

Answer 1

The area would be '15l - l²

Explanation:

Given,

By 30 feet of wire fencing we need to make a rectangular shape,

Thus, perimeter of such rectangle = 30 feet,

We know that,

Perimeter of a rectangle = 2( length + width)

if length = l feet,

⇒ 2(l + width) = 30

⇒ 2l + 2 × width = 30

⇒ 2 × width = 30 - 2l

⇒ width =
`(30-2l)/(2)` = (15-l) feet,

Now, area of the rectangle,

A = length × width

= l × (15-l)

= 15l - l²

Which is the required polynomial expression.

Note :

Polynomial expression : an expression having terms consisting coefficients and variables separated by addition, subtraction and multiplication.