The area A of a square varies directly as the square of its side 5

In this problem, the area \( A \) of a square varies directly as the square of its side length \( s \). This means we can express this relationship using the equation:

\[
A = k s^2
\]

Where:
- \( A \) is the area of the square,
- \( s \) is the side length,
- \( k \) is a constant of proportionality.

Now, according to the problem, the side length is 5 units. We can substitute \( s = 5 \) into the equation:

\[
A = k \times 5^2
\]
\[
A = 25k
\]

Without more information about the value of \( A \), we cannot determine the value of \( k \) directly, but the relationship \( A = 25k \) holds true as a formula. If you know the area \( A \), you can solve for \( k \) and find the specific area of the square.

Would you like to explore further details or another example with specific values?

Here are five questions to deepen the concept:
1. What is the constant \( k \) if the area of the square is 100 square units?
2. How would the formula change if the side length of the square doubled?
3. Can you express the relationship between the side length and the area in terms of a ratio?
4. What happens to the area if the side length is tripled?
5. How would the concept of "varying directly" differ if this were a rectangle instead of a square?

**Tip:** When a variable "varies directly" with another, it means any increase in one variable causes a proportional increase in the other.

The area A of a square varies directly as the square of its side 5.

Explore the concept of direct variation in geometry by calculating the area of a square with a side length of 5. Learn the formula A = k * s^2, which connects the area and the side length, suitable for Grades 6-8.

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