Write an expression for the perimeter of this triangle. Simplify your answer.
Understand the Problem
The question is asking for an expression that represents the perimeter of a triangle with sides given in terms of variables (5n, n, and 7). We need to add these expressions together and then simplify the result.
Answer
The perimeter is \( P = 6n + 7 \).
Answer for screen readers
The expression for the perimeter of the triangle is ( P = 6n + 7 ).
Steps to Solve
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Identify the sides of the triangle The triangle has three sides: ( 5n ), ( n ), and ( 7 ).
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Write the perimeter expression The perimeter ( P ) of a triangle is calculated by adding the lengths of all its sides: $$ P = 5n + n + 7 $$
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Combine like terms Combine the terms with ( n ): $$ P = (5n + n) + 7 $$ This simplifies to: $$ P = 6n + 7 $$
The expression for the perimeter of the triangle is ( P = 6n + 7 ).
More Information
The perimeter of a triangle represents the total length around the triangle. By using algebraic expressions for the sides, we can understand how changes in the variable ( n ) affect the perimeter.
Tips
- Forgetting to include all sides in the perimeter calculation. Ensure each side is added.
- Not simplifying correctly; combining like terms is crucial.
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