Question

the width of a rectangle measures (2d + 8) centimeters, and its length measures (7d - 2) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?

answer

18d + 12
20d + 10
6 + 9d
10d + 5

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, length is \( (7d - 2) \) and width is \( (2d + 8) \). So we first find the sum of length and width: \( (7d - 2)+(2d + 8) \).
Simplify the sum: \( 7d - 2 + 2d + 8 = (7d + 2d)+(-2 + 8)=9d + 6 \).

Step2: Multiply by 2 to get perimeter

Now, multiply this sum by 2 (from the perimeter formula): \( 2\times(9d + 6) \).
Using the distributive property \( a(b + c)=ab + ac \), we have \( 2\times9d + 2\times6 = 18d + 12 \).

Answer:

\( 18d + 12 \) (corresponding to the option "18d + 12")