Question

the rectangle below has an area of $x^{2}-16$ square meters and a width of $x + 4$ meters.
what expression represents the length of the rectangle?
length = meters

Explanation:

Step1: Recall the area formula for a rectangle

The area formula for a rectangle is \(A = \text{length}\times\text{width}\). So, \(\text{length}=\frac{A}{\text{width}}\). Here, \(A=x^{2}-16\) and \(\text{width}=x + 4\). Then \(\text{length}=\frac{x^{2}-16}{x + 4}\).

Step2: Factor the numerator

Use the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\). For \(x^{2}-16\), where \(a=x\) and \(b = 4\), we have \(x^{2}-16=(x + 4)(x - 4)\). So, \(\text{length}=\frac{(x + 4)(x - 4)}{x + 4}\).

Step3: Simplify the expression

Cancel out the common factor \((x + 4)\) (assuming \(x
eq-4\)). After canceling, we get \(\text{length}=x-4\).

Answer:

\(x - 4\)