The perimeter of an isosceles triangle is 36 feet. Each of the two congruent sides of the triangle has a...

1. TRANSLATE the problem information

• Given information:
  • Isosceles triangle has perimeter of 36 feet
  • Two congruent sides each measure 10 feet
  • Need to find the third side length

• What this tells us: We can set up an equation where all three side lengths sum to 36

2. TRANSLATE into a mathematical equation

• Let \(\mathrm{x}\) = length of third side
• Perimeter equation: \(10 + 10 + \mathrm{x} = 36\)
• This represents: (first congruent side) + (second congruent side) + (third side) = (total perimeter)

3. SIMPLIFY the equation

• Combine like terms: \(20 + \mathrm{x} = 36\)
• Subtract 20 from both sides: \(\mathrm{x} = 36 - 20\)
• Calculate: \(\mathrm{x} = 16\)

Answer: C. 16

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make arithmetic errors when solving the equation \(20 + \mathrm{x} = 36\)

Instead of correctly calculating \(\mathrm{x} = 36 - 20 = 16\), they might:

• Subtract incorrectly: \(36 - 20 = 14\) (not among choices, leading to guessing)
• Add instead of subtract: \(36 + 20 = 56\) (realizing this is too large, leading to confusion)
• Make other calculation mistakes that yield 12 or 18

This may lead them to select Choice B (12) or Choice D (18)

Second Most Common Error:

Missing conceptual knowledge: Students don't understand what "isosceles triangle" means

If they think all three sides are different lengths, they might get confused about how to set up the equation or might assume the third side is also 10 feet.

This may lead them to select Choice A (10)

The Bottom Line:

This problem tests whether students can translate a geometric word problem into a simple linear equation. The key challenge is maintaining accuracy through the translation and algebraic solving process, as small errors can lead to the wrong answer choices provided.