The area of a square is 64 square inches. What is the side length, in inches, of this square?

1. TRANSLATE the problem information

• Given information:
  • Area of square = 64 square inches
  • Need to find: side length in inches

2. INFER the approach

• To find side length from area, I need to use the relationship between them
• For a square, area and side length are connected by: \(\mathrm{A = s^2}\)
• This means I need to solve for s when A = 64

3. SIMPLIFY to solve for side length

• Set up the equation: \(\mathrm{64 = s^2}\)
• Take the square root of both sides: \(\mathrm{s = \sqrt{64} = 8}\)
• The side length is 8 inches

Answer: A. 8

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misread what the question is asking for and simply select the given area value.

They see "area is 64" and immediately choose 64 as their answer without recognizing that the question asks for side length, not area. This leads them to select Choice C (64).

Second Most Common Error:

Missing conceptual knowledge: Students don't remember or confuse the area formula for a square.

Without knowing \(\mathrm{A = s^2}\), they might guess at relationships like "side length = area ÷ 4" (thinking of perimeter) or make other incorrect connections. This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can distinguish between what's given (area) and what's asked for (side length), then apply the correct formula to connect them. The key is recognizing that you're working backwards from area to find the side length.