The perimeter of an equilateral triangle is 13 inches more than the perimeter of a​ square, and the side of the triangle is 7 inches longer than the side of the square. Find the side of the triangle

Let's denote:

- The side length of the equilateral triangle as \( t \).
- The side length of the square as \( s \).

### Given Information:
1. The perimeter of the equilateral triangle is 13 inches more than the perimeter of the square.
2. The side of the triangle is 7 inches longer than the side of the square.

### Step 1: Express the perimeters
- The perimeter of the equilateral triangle is \( 3t \).
- The perimeter of the square is \( 4s \).

### Step 2: Set up equations
From the problem statement, we have:

\[
3t = 4s + 13 \quad \text{(Equation 1)}
\]
\[
t = s + 7 \quad \text{(Equation 2)}
\]

### Step 3: Substitute Equation 2 into Equation 1
Substitute \( t = s + 7 \) into Equation 1:

\[
3(s + 7) = 4s + 13
\]

### Step 4: Expand and simplify the equation
Expanding the left-hand side:

\[
3s + 21 = 4s + 13
\]

Subtract \( 3s \) from both sides:

\[
21 = s + 13
\]

Subtract 13 from both sides:

\[
s = 8
\]

### Step 5: Find the side of the triangle
Using Equation 2:

\[
t = s + 7 = 8 + 7 = 15
\]

### Final Answer:
The side of the triangle is **15 inches**.

Would you like more details or have any questions about the steps? Here are some related questions:

1. What is the general formula for the perimeter of an equilateral triangle?
2. How can the relationship between side lengths and perimeters be used in different geometric shapes?
3. What if the triangle and square had different perimeter relationships?
4. Can this problem be solved graphically, and how?
5. What if the difference in side lengths was given instead of the perimeter difference?

**Tip:** Always double-check your substitutions in algebraic problems to avoid small mistakes that can lead to incorrect answers.

Learn how to find the side length of an equilateral triangle when its perimeter is 13 inches more than that of a square, and its side is 7 inches longer. Detailed step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation