Question

a square has sides of length s. A rectangle is 6 inches shorter and 1 inch longer than the square. which of the following polynomial represents the area of the rectangle?

Answer 1

The polynomial is (s+1)(s+6) or s^2+7s+6

:)

Answer 2

The polynomial equation that represents area of rectangle is:

`s^2-5s-6`

Explanation:

It is given that a square has side of length 's'.

A rectangle is 6 inches shorter and 1 inch longer than the square.

Let the sides of the rectangle are represented by 'a' and 'b'.

That means that a= (s-6) inches.

and b=(s+1) inches.

Let A denote the area of rectangle with sides a and b.

Hence, the area of rectangle is given by:

`A=a* b`

`A=(s-6)* (s+1)\\\\A=s(s+1)-6(s+1)\\\\A=s^2+s-6s-6\\\\A=s^2-5s-6`

The unit of area is 'square inches'

Hence, the polynomial equation that represents the area of the rectangle is:

`s^2-5s-6`