Question

Joe wants to add cucumbers to his garden and knows the rectangular area is represented by x^2 - 4x - 21 square units. What expressions would represent the length and width of the cucumber field?

Answer 1

Given:

The area of rectangular garden is
`x^2-4x-21` square units.

To find:

The length and width of the cucumber field.

Solution:

The area of a rectangle is:

`A=l* w`

Where l is length and w is width of the rectangle.

The area of rectangular garden is
`x^2-4x-21` square units.

We need to find the factors of
`x^2-4x-21` to get the length and width.

`A=x^2-4x-21`

Splitting the middle term, we get

`A=x^2-7x+3x-21`

`A=x(x-7)+3(x-7)`

`A=(x-7)(x+3)`

Area of a rectangle is the product of length and width.

Therefore, the length and width of the rectangle are
`(x-7)` units and
`(x+3)` units.