2.25x for the square
1.5x + 6 for the triangle
The perimeter for the square and the equilateral triangle are the same. What is the value of x

Given the problem:

1. The perimeter of the square is \( 2.25x \).
2. The perimeter of the equilateral triangle is \( 1.5x + 6 \).
3. The perimeters of the square and the equilateral triangle are the same.

We can set up the equation for the perimeters:
\[
2.25x = 1.5x + 6
\]

### Solving for \( x \):

1. Subtract \( 1.5x \) from both sides:
   \[
   2.25x - 1.5x = 6
   \]
   \[
   0.75x = 6
   \]

2. Divide both sides by 0.75:
   \[
   x = \frac{6}{0.75}
   \]
   \[
   x = 8
   \]

Thus, the value of \( x \) is \( \boxed{8} \).

---

Would you like more details, or do you have any questions about the process?  
Here are some related questions you might consider:

1. What would the side length of the square be if \( x = 8 \)?
2. How would you calculate the side length of the equilateral triangle?
3. What is the total perimeter of each shape when \( x = 8 \)?
4. If the perimeter of the triangle changed to \( 2x + 4 \), how would that affect \( x \)?
5. How does the perimeter of regular polygons change with side length?

**Tip:** Always set up the equation carefully by identifying the relationships between given shapes before solving.

The perimeter for the square and the equilateral triangle are the same. What is the value of x, given that the perimeter of the square is 2.25x and the perimeter of the equilateral triangle is 1.5x + 6?

Learn how to solve for x when the perimeter of a square (2.25x) equals the perimeter of an equilateral triangle (1.5x + 6). This algebra problem covers linear equations and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation