the length of a square can be expressed as 2x+3. if the area of the square is 121 square meters, what is the value of x?

We know the area of a square is given by the formula:

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

In this case, the side length of the square is expressed as \( 2x + 3 \), and the area is 121 square meters. So, we can set up the equation:

\[
(2x + 3)^2 = 121
\]

Now, solve for \( x \):

### Step 1: Take the square root of both sides

\[
2x + 3 = \pm \sqrt{121}
\]

\[
2x + 3 = \pm 11
\]

### Step 2: Solve for \( x \) for both cases

#### Case 1: \( 2x + 3 = 11 \)

\[
2x = 11 - 3
\]
\[
2x = 8
\]
\[
x = \frac{8}{2} = 4
\]

#### Case 2: \( 2x + 3 = -11 \)

\[
2x = -11 - 3
\]
\[
2x = -14
\]
\[
x = \frac{-14}{2} = -7
\]

So, the two possible values of \( x \) are \( x = 4 \) and \( x = -7 \).

However, since a side length cannot be negative, we reject \( x = -7 \). Thus, the value of \( x \) is:

\[
x = 4
\]

Would you like more details or have any further questions?

Here are 5 questions for further exploration:
1. How would the problem change if the area of the square was different, say 225 square meters?
2. What happens if the expression for the side length includes a negative term, such as \( -2x + 3 \)?
3. Can you solve the equation if the side length is given in terms of a more complex polynomial, e.g., \( 3x^2 + 2x + 1 \)?
4. What if the figure is not a square but a rectangle with the same expression for length?
5. How do you find the perimeter of the square once you know the value of \( x \)?

**Tip:** Always check if the solution makes sense in the context of the problem, such as rejecting negative side lengths for a square!

The length of a square can be expressed as 2x+3. If the area of the square is 121 square meters, what is the value of x?

Learn how to solve for x when the side length of a square is given as 2x+3 and the area is 121 square meters. This detailed step-by-step solution covers key algebraic and geometric concepts suitable for students in Grades 7-10.

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