Question

A square has side length units. What is its area?

Responses

square units
x 2 + 25 square units

square units
x 2 − 25 square units

square units
x 2 + 10 x + 25 square units

square units
x 2 − 10 x + 25 square units

Answer 1

The area \( A \) of a square can be calculated using the formula:

\[
A = \text{side length}^2
\]

If the side length of the square is given as \( x \) units, then the area is:

\[
A = x^2 \text{ square units}
\]

Now let's analyze the responses given:

1. **Response 1:** \( x^2 + 25 \) square units (not correct)
2. **Response 2:** \( x^2 - 25 \) square units (not correct)
3. **Response 3:** \( x^2 + 10x + 25 \) square units (which can be factored as \( (x + 5)^2 \), representing the area of a square with side length \( x + 5 \), not just \( x \))
4. **Response 4:** \( x^2 - 10x + 25 \) square units (this is \( (x - 5)^2 \), representing the area of a square with side length \( x - 5 \), not just \( x \))

None of the provided responses represent the area of a square with side length \( x \) correctly, which should solely be \( x^2 \) square units.