Question

the width of a rectangle measures $(8u - 4)$ centimeters, and its length measures $(8u - 2)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer $12 + 8u$ $-12 + 32u$ $-6 + 16u$ $4u + 6$ submit answer

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 length and width into the formula

Given \(l=(8u - 2)\) and \(w=(8u - 4)\). Then \(P = 2[(8u - 2)+(8u - 4)]\).

Step3: Simplify the expression inside the brackets

\((8u - 2)+(8u - 4)=8u+8u-2 - 4=16u-6\).

Step4: Multiply by 2

\(P = 2(16u - 6)\). Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b = 16u\), \(c=-6\)), we get \(P=2\times16u-2\times6 = 32u-12=-12 + 32u\).

Answer:

-12 + 32u