If the are of the square is (4x^2 - 4x + 1)cm^2, what is the measurement of it's side

To find the measurement of the side of a square given its area, we need to take the square root of the area.

Given the area of the square is:

\[
\text{Area} = (4x^2 - 4x + 1) \text{ cm}^2
\]

The side length \( s \) of the square is the square root of the area:

\[
s = \sqrt{4x^2 - 4x + 1}
\]

Now, let's simplify the expression inside the square root. The expression \( 4x^2 - 4x + 1 \) is a perfect square trinomial. We can factor it as:

\[
4x^2 - 4x + 1 = (2x - 1)^2
\]

Therefore, the side length \( s \) becomes:

\[
s = \sqrt{(2x - 1)^2}
\]

Since we are dealing with lengths, which are non-negative, we take the positive square root:

\[
s = |2x - 1|
\]

Thus, the measurement of the side of the square is:

\[
\boxed{|2x - 1| \text{ cm}}
\]

This means the side length is \(2x - 1\) if \(2x - 1 \geq 0\), or \(1 - 2x\) if \(2x - 1 < 0\).

Would you like more details or have any questions?

### Related Questions:
1. What happens if \( x = \frac{1}{2} \)? What would be the side length?
2. How do you find the side length if the area is expressed differently?
3. How can you determine if the side length is a whole number for specific values of \( x \)?
4. What if the area is not a perfect square trinomial? How would you find the side length?
5. Can you derive the formula for the area of a square given any side length?

**Tip:** When solving for unknowns, always check if the expression can be simplified, such as factoring to identify perfect squares.

If the area of the square is (4x^2 - 4x + 1) cm^2, what is the measurement of its side?

Learn how to determine the side length of a square with an area of (4x^2 - 4x + 1) cm². This solution explains key algebraic concepts, such as factoring perfect square trinomials and applying square root properties. Suitable for Grades 9-11 students.

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