A kite has two pairs of congruent adjacent sides. The perimeter of the kite is 44 centimeters. Each of the...

1. TRANSLATE the problem information

• Given information:
  • Kite has two pairs of congruent adjacent sides
  • Total perimeter = 44 centimeters
  • Each shorter side = 8 centimeters
  • Need to find each longer side length

• What this tells us: We have four sides total, with two sides being 8 cm each, and two unknown sides of equal length

2. INFER the kite structure

• A kite has exactly four sides arranged as two pairs of equal adjacent sides
• If shorter sides are 8 cm each, then longer sides must both be the same unknown length
• Let \(\mathrm{x}\) = length of each longer side

3. TRANSLATE to create the perimeter equation

• The four sides are: 8, 8, x, and x
• Perimeter = sum of all sides: \(\mathrm{8 + 8 + x + x = 44}\)

4. SIMPLIFY the equation

• Combine like terms: \(\mathrm{16 + 2x = 44}\)
• Subtract 16 from both sides: \(\mathrm{2x = 28}\)
• Divide by 2: \(\mathrm{x = 14}\)

Answer: B (14)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand the structure of a kite and assume all four sides could be different lengths, or think there are only two sides total (one short, one long).

This confusion leads them to set up incorrect equations like "\(\mathrm{8 + x = 44}\)" (thinking there are only two sides), giving \(\mathrm{x = 36}\), which isn't even an answer choice. This causes them to get stuck and randomly guess.

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify that there are four sides but incorrectly set up the equation as "\(\mathrm{2(8) + x = 44}\)" thinking there's only one longer side instead of two.

This gives \(\mathrm{16 + x = 44}\), so \(\mathrm{x = 28}\). This leads them to select Choice D (28).

The Bottom Line:

This problem requires students to clearly understand what "two pairs of congruent adjacent sides" means in the context of a four-sided figure. The key insight is recognizing that "pairs" means there are two of each length, creating exactly four sides total.