Final answer:
The width of the rectangle is option (b) (x-3)(x+3). This is because, when divided by the length (3x^2+5), it reduces to a form that can come from dividing the area (3x^4) by 3x^2, resulting in x^2 - 9.
Correct option is b.
Step-by-step explanation:
To find the width of a rectangle when given the area and the length, you would divide the area by the length. The area of the rectangle is given as 3x^4 and the length as 3x^2+5. So, the width w can be found by the equation w = ÷(3x^2+5). However, when we perform the division, the expression should simplify to a form that does not depend on + or − a constant like 5 since the original area doesn't contain such a term. Thus, option (d) (x^2+9) cannot be correct because adding 9 doesn't align with the given area.
The correct width of the rectangle is option (b) (x-3)(x+3), which is derived from the factored form of the area 3x^4. When you divide 3x^4 by the length 3x^2+5, you should get a result that is a polynomial. Among the options given, option (b) is factorable and can reduce to x^2 - 9 when divided by 3, which can be a simplified form of the original area when divided by the length 3x^2.
Correct option is b.