Question

the rectangle below has an area of $x^{2}+13x + 36$ square meters and a length of $x + 9$ meters. what expression represents the width of the rectangle? width = meters

Explanation:

Step1: Recall the area formula for rectangle

The area of a rectangle is \(A = \text{length}\times\text{width}\). So, \(\text{width}=\frac{A}{\text{length}}\). Given \(A=x^{2}+13x + 36\) and \(\text{length}=x + 9\).

Step2: Factor the quadratic expression

Factor \(x^{2}+13x + 36\). We need to find two numbers that multiply to \(36\) and add up to \(13\). The numbers are \(9\) and \(4\). So, \(x^{2}+13x + 36=(x + 9)(x+4)\).

Step3: Calculate the width

Since \(\text{width}=\frac{(x + 9)(x + 4)}{x + 9}\), cancel out the common factor \((x + 9)\) (assuming \(x
eq - 9\)).

Answer:

\(x + 4\)