Question

yellow: the length of a rectangle is represented by (2x - 7) and its width by (x² - 4x). what expression would represent the perimeter of the rectangle?

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width.

Step2: Substitute the given expressions for length and width

Given \(l=(2x - 7)\) and \(w=(x^{2}-4x)\). Then \(P = 2((2x - 7)+(x^{2}-4x))\).

Step3: Simplify the expression inside the parentheses

First, combine like - terms inside the parentheses: \((2x - 7)+(x^{2}-4x)=x^{2}+(2x-4x)-7=x^{2}-2x - 7\).

Step4: Distribute the 2

Now, distribute the 2 across the simplified expression: \(P = 2(x^{2}-2x - 7)=2x^{2}-4x-14\).

Answer:

\(2x^{2}-4x - 14\)