The problem describes the sides of a triangle and asks us to determine the correct equation that represents the problem. Here's a breakdown:

Problem Analysis:

• Shortest side: $s$
• Longest side: $s + 8$ (8 cm longer than the shortest side)
• Third side: 12 cm
• Perimeter: $38$ cm

The perimeter is the sum of all three sides. Therefore, the equation representing the problem is: $s + (s + 8) + 12 = 38$

Simplify the equation:

1. Combine like terms: $2s + 8 + 12 = 38$ $2s + 20 = 38$

This matches the first option in the multiple-choice list: $s + s + 8 + 12 = 38$.

Would you like me to solve for $s$ or explain further?

5 Related Questions:

1. How do you solve equations with variables on both sides?
2. What are the steps to combine like terms in an equation?
3. How is the perimeter of a polygon calculated in general?
4. How would the equation change if the perimeter was a different value?
5. How can this problem be represented graphically?

Tip:

Always label each part of the problem clearly when translating word problems into equations to avoid confusion.