A right triangle has legs of length 13 feet and 11 feet. What is the square of the length of...

1. TRANSLATE the problem information

• Given information:
  • Right triangle with legs of 13 feet and 11 feet
  • Need to find the square of the hypotenuse length
• This tells us we need to use the Pythagorean theorem: \(\mathrm{c^2 = a^2 + b^2}\)

2. TRANSLATE the setup

• In the Pythagorean theorem:
  • \(\mathrm{a = 13}\) feet (first leg)
  • \(\mathrm{b = 11}\) feet (second leg)
  • \(\mathrm{c^2}\) = what we're looking for (square of hypotenuse)

3. SIMPLIFY by calculating the squares

• Calculate \(\mathrm{13^2 = 169}\)
• Calculate \(\mathrm{11^2 = 121}\)
• Add them: \(\mathrm{c^2 = 169 + 121 = 290}\)

Answer: C (290)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what the Pythagorean theorem requires and add the legs directly instead of adding their squares.

They think: 'I need the hypotenuse, so \(\mathrm{13 + 11 = 24}\), then \(\mathrm{24^2 = 576}\)'

This leads them to select Choice D (576)

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the problem correctly but make arithmetic errors when squaring the numbers.

Common mistakes include miscalculating \(\mathrm{13^2}\) or \(\mathrm{11^2}\), or making addition errors when combining 169 + 121.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can properly translate a word problem into the Pythagorean theorem and execute the arithmetic accurately. The key insight is recognizing that we want \(\mathrm{c^2}\) directly, not c, which makes the calculation straightforward once properly set up.