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?
width = meters

Explanation:

Step1: Recall the area formula for a rectangle

The area of a rectangle is \(A = \text{length}\times\text{width}\). So, \(\text{width}=\frac{A}{\text{length}}\). Here, \(A=x^{2}-15x + 56\) and \(\text{length}=x - 7\).

Step2: Factor the quadratic expression

Factor \(x^{2}-15x + 56\). We need 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: Calculate the width

Since \(\text{width}=\frac{x^{2}-15x + 56}{x - 7}\) and \(x^{2}-15x + 56=(x - 7)(x - 8)\), then \(\text{width}=\frac{(x - 7)(x - 8)}{x - 7}\). Cancel out the common factor \((x - 7)\) (assuming \(x
eq7\)).

Answer:

\(x - 8\)