Question

the rectangle below has an area of ( x^2 - 11x + 30 ) square meters and a length of ( x - 5 ) meters. what expression represents the width of the rectangle? image of a green rectangle labeled with length ( x - 5 ), area ( x^2 - 11x + 30 ), and \width\ on the left side width = blank ( \frac{+x}{-x} ) meters

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). So, to find the width, we use \( \text{width} = \frac{A}{\text{length}} \). Here, \( A = x^2 - 11x + 30 \) and length \( = x - 5 \), so we need to divide \( x^2 - 11x + 30 \) by \( x - 5 \).

Step2: Factor the quadratic expression

Factor \( x^2 - 11x + 30 \). We need two numbers that multiply to 30 and add to -11. Those numbers are -5 and -6. So, \( x^2 - 11x + 30=(x - 5)(x - 6) \).

Step3: Divide the factored form by length

Now, divide \( (x - 5)(x - 6) \) by \( x - 5 \). Canceling out the common factor \( x - 5 \) (assuming \( x
eq5 \)), we get \( x - 6 \).

Answer:

\( x - 6 \)