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?

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. So, $w=\frac{A}{l}$.

Step2: Factor the area 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 $w=\frac{A}{l}$ and $A=(x - 7)(x - 8)$, $l=x - 7$, then $w=\frac{(x - 7)(x - 8)}{x - 7}$. Canceling out the common factor $(x - 7)$ (assuming $x
eq7$), we get $w=x - 8$.

Answer:

$x - 8$