Question

the rectangle below has an area of $x^{2}-7x + 10$ square meters and a width of $x - 5$ meters. what expression represents the length of the rectangle? length $= square$ meters

Explanation:

Step1: Recall the formula for the area of a rectangle

The area of a rectangle is \(A = \text{length}\times\text{width}\). So, \(\text{length}=\frac{A}{\text{width}}\). Here, \(A=x^{2}-7x + 10\) and \(\text{width}=x - 5\).

Step2: Factor the quadratic expression

Factor \(x^{2}-7x + 10\). We need 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: Divide the factored area by the width

\(\text{length}=\frac{(x - 2)(x - 5)}{x - 5}\). Since \(x
eq5\) (because if \(x = 5\), the width \(x-5=0\)), we can cancel out the \((x - 5)\) terms.

Answer:

\(x-2\)