Question

the rectangle below has an area of $x^{2}-6x - 7$ square meters and a width of $x - 7$ meters. what expression represents the length of the rectangle? length $x^{2}-6x - 7$ length = meters

Explanation:

Step1: Recall area formula

The area of a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. Given $A=x^{2}-6x - 7$ and $w=x - 7$, then $l=\frac{A}{w}=\frac{x^{2}-6x - 7}{x - 7}$.

Step2: Factor the numerator

Factor $x^{2}-6x - 7$. We need two numbers that multiply to $-7$ and add up to $-6$. The numbers are $-7$ and $1$. So $x^{2}-6x - 7=(x - 7)(x+1)$.

Step3: Simplify the fraction

Substitute the factored form into the fraction: $\frac{(x - 7)(x + 1)}{x - 7}$. Cancel out the common factor $(x - 7)$ (assuming $x
eq7$). We get $l=x + 1$.

Answer:

$x + 1$