The length of a rectangle is 20 units more than its width. The area of the rectangle is x4 - 100.Which statement about the width of the rectangle is true?x2 – 10 because the area expression can be rewritten as (x2 – 10)( x2 + 10) which equals (x2 – 10)((x2 – 10) + 20).x2 + 10 because the area expression can be rewritten as (x2 + 10)( x2 – 10) which equals (x2 + 10)((x2 + 10) – 20).x2 – 30 because the area expression can be rewritten as (x2 + 10)( x2 – 10) which equals (x2 + 10)((x2 – 30) + 20).x2 + 30 because the area expression can be rewritten as (x2 – 10)( x2 + 10) which equals (x2 – 10)((x2 + 30) – 20).

To solve the problem, let's break it down step by step:

1. Identify the given information:

   • The length of the rectangle is 20 units more than its width.
   • The area of the rectangle is given by the expression $x^4 - 100$.

2. Express the length and width in terms of a variable:

   • Let the width of the rectangle be $w$.
   • Then, the length of the rectangle is $w + 20$.

3. Set up the equation for the area:

   • The area of the rectangle is given by the product of its length and width.
   • Therefore, $w \times (w + 20) = x^4 - 100$.

4. Factor the given area expression:

   • The expression $x^4 - 100$ can be factored using the difference of squares: $x^4 - 100 = (x^2 - 10)(x^2 + 10)$

5. Match the factored form to the product of width and length:

   • We need to match $w \times (w + 20)$ to $(x^2 - 10)(x^2 + 10)$.

6. Compare the factors:

   • If we let $w = x^2 - 10$, then the length $w + 20$ becomes: $(x^2 - 10) + 20 = x^2 + 10$
   • This matches the factored form $(x^2 - 10)(x^2 + 10)$.

Therefore, the correct statement about the width of the rectangle is:

• $x^2 - 10$ because the area expression can be rewritten as $(x^2 - 10)(x^2 + 10)$ which equals $(x^2 - 10)((x^2 - 10) + 20)$.