https://file.aiquickdraw.com/mathbot/file/17266247203816sfu0ypo.jpg

Given:

- The perimeter of the triangle is \( P = 16x - 1 \).
- The perimeter of the square is \( 4 \times (3x - 2) \) since all four sides of a square are equal.

### Step 1: Set up the equation

Since the perimeter of the triangle is equal to the perimeter of the square, we have:

\[
16x - 1 = 4 \times (3x - 2)
\]

### Step 2: Expand the right side of the equation

\[
16x - 1 = 12x - 8
\]

### Step 3: Solve for \( x \)

1. Subtract \( 12x \) from both sides:

\[
16x - 12x - 1 = -8
\]

This simplifies to:

\[
4x - 1 = -8
\]

2. Add 1 to both sides:

\[
4x = -7
\]

3. Divide by 4:

\[
x = -\frac{7}{4}
\]

### Final Answer

\[
x = -\frac{7}{4}
\]

Would you like a more detailed explanation or have any questions?

### Follow-Up Questions

1. What is the perimeter of the triangle when \( x = -\frac{7}{4} \)?
2. What is the perimeter of the square when \( x = -\frac{7}{4} \)?
3. How do you find the perimeter of different polygons given their side lengths?
4. Why does setting the two perimeters equal to each other help find the value of \( x \)?
5. How does changing the value of \( x \) affect the perimeter of the triangle and square?

### Tip

When solving an equation, always simplify each side as much as possible before isolating the variable.

The perimeter of the triangle is equal to the perimeter of the square. The perimeter of the triangle is P = 16x - 1, and the perimeter of the square is 4(3x - 2). Write and solve an equation to find the value of x.

Learn how to solve a perimeter equation where the perimeter of a triangle (P = 16x - 1) equals the perimeter of a square (4 times the side length, 3x - 2). Follow a step-by-step algebraic solution, ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation