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?

Explanation:

Step1: Recall area formula

The area of a rectangle $A = l\times w$, where $l$ is length and $w$ is width. Given $A=x^{2}-16$ and $w = x + 4$, then $l=\frac{A}{w}=\frac{x^{2}-16}{x + 4}$.

Step2: Factor the numerator

We know that $x^{2}-16$ is a difference - of - squares, and $x^{2}-16=(x + 4)(x - 4)$ according to the formula $a^{2}-b^{2}=(a + b)(a - b)$ where $a=x$ and $b = 4$.

Step3: Simplify the fraction

Substitute $x^{2}-16=(x + 4)(x - 4)$ into $\frac{x^{2}-16}{x + 4}$, we get $\frac{(x + 4)(x - 4)}{x + 4}$. Since $x
eq - 4$ (otherwise the width is 0), we can cancel out the common factor $(x + 4)$ and the result is $x-4$.

Answer:

$x - 4$