Question

the rectangle below has an area of $x^{2}-4x - 12$ square meters and a length of $x + 2$ meters.
what expression represents the width of the rectangle?
width $=$ meters

Explanation:

Step1: Recall the formula for the area of a rectangle

The area of a rectangle \(A = \text{length}\times\text{width}\). Given \(A=x^{2}-4x - 12\) and \(\text{length}=x + 2\), then \(\text{width}=\frac{A}{\text{length}}=\frac{x^{2}-4x - 12}{x + 2}\).

Step2: Factor the numerator

Factor \(x^{2}-4x - 12\). We need two numbers \(a\) and \(b\) such that \(a\times b=-12\) and \(a + b=-4\). The numbers are \(a = 2\) and \(b=-6\). So \(x^{2}-4x - 12=(x + 2)(x-6)\).

Step3: Simplify the fraction

Substitute the factored form into the width formula: \(\frac{(x + 2)(x-6)}{x + 2}\). Cancel out the common factor \((x + 2)\) (assuming \(x
eq - 2\)).

Answer:

\(x-6\)