Simplifying Expressions - Perimeter Of A Triangle

🔑 Key Concepts

  • The perimeter of a triangle is the sum of its three side lengths.
  • Side lengths written as algebraic expressions can be added to create a perimeter expression.
  • Like terms must have identical variable parts before they can be combined.
  • Combine the variable terms and constants separately.
  • Substitute the given value of the variable after simplifying the expression.
  • The final perimeter must include the correct unit of measure.

✏️ Worked Example — Simplifying and Evaluating a Triangle Perimeter Expression

🧠 Math Vocabulary

  • Perimeter: The total distance around a two-dimensional figure.
  • Algebraic expression: A mathematical phrase containing numbers, variables, and operations.
  • Term: A number, variable, or product separated from other terms by addition or subtraction.
  • Coefficient: The number multiplying a variable, such as the \(4\) in \(4x\).
  • Constant: A number without a variable, such as \(5\), \(7\), or \(1\).
  • Like terms: Terms that have identical variable parts.
  • Simplify: To rewrite an expression in an equivalent form with no remaining like terms to combine.
  • Substitution: Replacing a variable with a known value.
  • Evaluate: To calculate the numerical value of an expression.
  • Equivalent expressions: Expressions that have the same value for every possible value of their variables.

💡 Main Idea

To find the perimeter of a triangle with algebraic side lengths, add the expressions for all three sides. Combine like terms to create a simpler equivalent expression, and then substitute the given value of the variable. For this triangle, \((x+5)+(2x+7)+(4x+1)\) simplifies to \(7x+13\). When \(x=4\), the perimeter is \(41\text{ cm}\).

📚 What You Should Already Know

Before this lesson, students should understand how perimeter is found, how to identify terms and coefficients, and how to combine like terms. Students should also know how to substitute a number for a variable and evaluate a numerical expression.

🚀 What Comes Next

Next, students can write and simplify perimeter expressions for rectangles and other polygons, compare equivalent expressions, and solve for unknown dimensions. These skills also support work with area, algebraic modeling, and multi-step equations.

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