Question

The area of a rectangular rug is given by the trinomial r^2-4r-21. What are the possible dimensions of the rug?

Answer 1

There are two possible values for r (area): r =-7 or r=3

Explanation:

Given the rectangular rug area is:

`r^(2) -4r -21`

We have to convert the above equation into factored form.

So two numbers whose product is -21r² and sum is -4r

<=>
`r^(2) -4r -21`

=
`r^(2) -7r + 3r -21`

= r (r -7) + 3(r -7)

= (r-7)(r+3)

We set
`r^(2) -4r -21` = 0

<=> (r-7)(r+3) = 0

<=> (r-7) = 0 or (r+3) = 0

<=> r =-7 or r=3

So, there are two possible values for r (area): r =-7 or r=3