Question

the width of a rectangle measures $(t - 8)$ centimeters, and its length measures $(5t + 6)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
$6t - 2$
$11 - 7t$
$22 - 14t$
$12t - 4$
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Explanation:

Step1: Recall the formula for the perimeter of a rectangle

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

Step2: Substitute the given expressions for length and width

Here, \(l=(5t + 6)\) and \(w=(t - 8)\). So, \(P=2[(5t + 6)+(t - 8)]\).

Step3: Simplify the expression inside the brackets

$$
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$$

Step4: Multiply by 2

\(P = 2(6t - 2)=12t-4\)

Answer:

\(12t - 4\)