Miss Yang has bulletin boards of different sizes in her classroom. She wants to calculate how much border she needs for each one. The length of each bulletin board is 6 inches less than three times its width, w

Question

. Simplify w + 3w − 6 + w + 3w − 6
to find the formula for the perimeter of each of Miss Yang’s bulletin boards.(1 point)
Responses

8w2 − 12
8 w squared minus 12

6w − 10
6 w minus 10

6w2 − 10
6 w squared minus 10

8w − 12

Answer 1

To find the formula for the perimeter of each of Miss Yang's bulletin boards given the length in terms of the width, we can start with the information provided.

The length \( l \) is given by: \[ l = 3w - 6 \]

The perimeter \( P \) of a rectangle can be calculated using the formula: \[ P = 2l + 2w \]

Substituting the expression for the length into the perimeter formula: \[ P = 2(3w - 6) + 2w \]

Now, let's simplify this:

1. Distribute the 2 in the first term: \[ P = 6w - 12 + 2w \]
2. Combine like terms: \[ P = (6w + 2w) - 12 \] \[ P = 8w - 12 \]

Thus, the simplified expression for the perimeter of each of Miss Yang's bulletin boards is: \[ \boxed{8w - 12} \]