Recalling the Formula for the Area of a Square

Oct 13, 2025 by recoveryshake.com 34 views

Introduction

In mathematics, the side length of a square is a crucial concept that is used to calculate the area and perimeter of the square. The side length of a square can be expressed in various forms, including algebraic expressions. In this article, we will explore how to find the value of x when the side length of a square is expressed as 2x + 3 and the area of the square is given as 121 square meters.

Understanding the Problem

The problem states that the side length of a square can be expressed as 2x + 3. This means that the side length of the square is a linear function of x. The area of the square is given as 121 square meters. We need to find the value of x that satisfies this condition.

Recalling the Formula for the Area of a Square

The area of a square is given by the formula A = s^2, where A is the area and s is the side length of the square. In this case, the area of the square is 121 square meters, so we can write:

121 = (2x + 3)^2

Expanding the Equation

To solve for x, we need to expand the equation (2x + 3)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we can expand the equation as follows:

(2x + 3)^2 = (2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9

Substituting the Value of the Area

Now that we have expanded the equation, we can substitute the value of the area, which is 121 square meters:

121 = 4x^2 + 12x + 9

Rearranging the Equation

To solve for x, we need to rearrange the equation to get a quadratic equation in x. We can do this by subtracting 121 from both sides of the equation:

0 = 4x^2 + 12x - 112

Solving the Quadratic Equation

Now that we have a quadratic equation in x, we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 4, b = 12, and c = -112. Plugging these values into the quadratic formula, we get:

x = (-(12) ± √((12)^2 - 4(4)(-112))) / 2(4) = (-12 ± √(144 + 1792)) / 8 = (-12 ± √1936) / 8 = (-12 ± 44) / 8

Finding the Value of x

Now that we have two possible values for x, we can find the value of x that satisfies the condition. We can do this by simplifying the two possible values for x:

x = (-12 + 44) / 8 or x = (-12 - 44) / 8 = 32 / 8 or x = -56 / 8 = 4 or x = -7

Conclusion

In this article, we have explored how to find the value of x when the side length of a square is expressed as 2x + 3 and the area of the square is given as 121 square meters. We have used the formula for the area of a square and the quadratic formula to solve for x. The value of x that satisfies the condition is x = 4.

Final Answer

Introduction

In our previous article, we explored how to find the value of x when the side length of a square is expressed as 2x + 3 and the area of the square is given as 121 square meters. In this article, we will answer some of the most frequently asked questions related to this topic.

Q: What is the formula for the area of a square?

A: The formula for the area of a square is A = s^2, where A is the area and s is the side length of the square.

Q: How do I find the side length of a square when the area is given?

A: To find the side length of a square when the area is given, you can use the formula s = √A, where s is the side length and A is the area.

Q: What is the difference between the side length and the area of a square?

A: The side length of a square is the length of one of its sides, while the area of a square is the total amount of space inside the square.

Q: Can I use the quadratic formula to solve for x in this problem?

A: Yes, you can use the quadratic formula to solve for x in this problem. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation.

Q: What is the value of x in this problem?

A: The value of x in this problem is x = 4.

Q: How do I check my answer to make sure it is correct?

A: To check your answer, you can plug the value of x back into the original equation and make sure it is true. In this case, you can plug x = 4 back into the equation 121 = (2x + 3)^2 and make sure it is true.

Q: What if I get a negative value for x?

A: If you get a negative value for x, it means that the value of x is not a solution to the equation. In this case, you can try plugging the negative value back into the original equation and see if it is true.

Q: Can I use this method to solve for x in other problems?

A: Yes, you can use this method to solve for x in other problems where the side length of a square is expressed as an algebraic expression and the area is given.

Q: What are some common mistakes to avoid when solving for x?

A: Some common mistakes to avoid when solving for x include:

Not checking your answer to make sure it is correct
Not using the correct formula for the area of a square
Not plugging the value of x back into the original equation to check your answer
Not considering negative values for x

Conclusion

In this article, we have answered some of the most frequently asked questions related to finding the value of x when the side length of a square is expressed as 2x + 3 and the area of the square is given as 121 square meters. We hope that this article has been helpful in clarifying any confusion and providing a better understanding of the topic.

Final Answer

The final answer is x = 4.