Question

the rectangle below has an area of x² - 7x + 10 square meters and a width of x - 5 meters. what expression represents the length of the rectangle? length = meters

Explanation:

Step1: Recall area formula for rectangle

The area formula of a rectangle is $A = l\times w$, where $A$ is the area, $l$ is the length and $w$ is the width. Given $A=x^{2}-7x + 10$ and $w=x - 5$.

Step2: Factor the area expression

We factor the quadratic expression $x^{2}-7x + 10$. We need to find two numbers that multiply to $10$ and add up to $-7$. The numbers are $-2$ and $-5$. So $x^{2}-7x + 10=(x - 2)(x - 5)$.

Step3: Find the length

Since $A=l\times w$, then $l=\frac{A}{w}$. Substituting $A=(x - 2)(x - 5)$ and $w=x - 5$ (assuming $x
eq5$), we get $l=x - 2$.

Answer:

$x - 2$