Question

the rectangle below has an area of ( x^2 - 15x + 56 ) square meters and a length of ( x - 7 ) meters. what expression represents the width of the rectangle? ( x - 7 ) image of green rectangle with \width\ label and ( x^2 - 15x + 56 ) inside width = blank meters. related content factoring quadratics as (x+a)(x+b) 6:34

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 \( \text{width} = \frac{\text{area}}{\text{length}} \).

Step2: Factor the quadratic expression

We need to factor \( x^2 - 15x + 56 \). We look for two numbers that multiply to \( 56 \) and add up to \( -15 \). The numbers are \( -7 \) and \( -8 \), so \( x^2 - 15x + 56=(x - 7)(x - 8) \).

Step3: Divide the area by the length

The length is \( x - 7 \), so the width is \( \frac{(x - 7)(x - 8)}{x - 7} \). Canceling out the common factor \( x - 7 \) (assuming \( x
eq7 \)), we get \( x - 8 \).

Answer:

\( x - 8 \)