write an equation of a square the length of the square is 5x+2 and the perimeter is 48

To find the equation, let's break down the information provided:

1. **Side length of the square:** \( 5x + 2 \)
2. **Perimeter of the square:** 48

The perimeter of a square is given by the formula:
\[
P = 4 \times \text{side length}
\]

Substitute the values into the formula:
\[
48 = 4 \times (5x + 2)
\]

Now, let's solve for \( x \):

1. Distribute the 4:
   \[
   48 = 20x + 8
   \]

2. Subtract 8 from both sides to isolate terms with \( x \):
   \[
   48 - 8 = 20x
   \]

   \[
   40 = 20x
   \]

3. Divide by 20 to solve for \( x \):
   \[
   x = \frac{40}{20} = 2
   \]

So, the value of \( x \) is 2.

To write the equation clearly:
\[
4 \times (5x + 2) = 48
\]

This equation relates the side length of the square to its perimeter.

**Would you like further details or have any questions?**

Here are 5 related questions to explore further:

1. What would be the area of the square using the value of \( x \)?
2. How would the perimeter change if the side length was increased by a constant value?
3. What if the perimeter was given, but the area was needed instead?
4. Can this method be used to find \( x \) if the shape was a rectangle instead?
5. How does changing the coefficient of \( x \) in the side length affect the perimeter?

**Tip:** When solving equations involving shapes, always start by recalling the fundamental properties and formulas of those shapes.

Learn how to set up and solve the equation of a square where the side length is 5x+2 and the perimeter is 48. This step-by-step guide covers basic algebraic and geometric concepts, ideal for students in Grades 6-8.

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