Find the perimeter. Simplify your answer.
Understand the Problem
The question is asking for the perimeter of a rectangle where the width is represented as 'b - 6' and the height is 2. To find the perimeter, we will use the formula P = 2(length + width). In this case, we will substitute the values and simplify the answer.
Answer
The perimeter of the rectangle is \( P = 2b - 8 \).
Answer for screen readers
The perimeter of the rectangle is ( P = 2b - 8 ).
Steps to Solve
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Identify dimensions The width of the rectangle is given as ( b - 6 ) and the height is 2.
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Apply the perimeter formula The formula for the perimeter ( P ) of a rectangle is given by: $$ P = 2(\text{length} + \text{width}) $$
In this case, substituting the given dimensions (height as length and width) into the formula: $$ P = 2(2 + (b - 6)) $$
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Simplify the expression Now, simplify the equation: [ P = 2(2 + b - 6) ] Combine like terms: [ P = 2(b - 4) ]
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Final simplification Distributing the 2: $$ P = 2b - 8 $$
The perimeter of the rectangle is ( P = 2b - 8 ).
More Information
This formula allows us to see how the perimeter changes with varying values of ( b ). If ( b ) increases, the perimeter will also increase linearly.
Tips
- Forgetting to apply the perimeter formula correctly. Always remember the correct formula ( P = 2(length + width) ).
- Not simplifying the expression after substituting the values. It is essential to combine like terms carefully.
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