Question

the width of a rectangle measures $(9s + 6)$ centimeters, and its length measures $(s + 1)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer $15s + 2$ $7 + 10s$ $14 + 20s$ $4 + 30s$

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 \(w=(9s + 6)\) and \(l=(s + 1)\), we substitute into the formula:
\(P=2((s + 1)+(9s + 6))\)

Step3: Simplify the expression inside the parentheses

\((s + 1)+(9s + 6)=s+9s + 1 + 6=10s+7\)

Step4: Multiply by 2

\(P = 2(10s + 7)=2\times10s+2\times7 = 20s+14\) or \(14 + 20s\)

Answer:

\(14 + 20s\)