The lengths of the three sides of a triangle (in inches) are consecutive odd integers. If the perimeter is 63 inches, find the value of the shortest of the three side lengths.

To solve this problem, let's denote the three sides of the triangle as \( x \), \( x+2 \), and \( x+4 \), where \( x \) represents the shortest side (as all three sides are consecutive odd integers).

Given that the perimeter of the triangle is 63 inches, we can set up the following equation:

\[
x + (x + 2) + (x + 4) = 63
\]

Simplify and solve for \( x \):

\[
3x + 6 = 63
\]

Subtract 6 from both sides:

\[
3x = 57
\]

Divide by 3:

\[
x = 19
\]

Therefore, the value of the shortest side is **19 inches**.

Would you like details or have any questions? Here are 5 related questions:

1. What would the side lengths be if the perimeter was 75 inches?
2. How do you determine if a set of side lengths can form a valid triangle?
3. What is the formula for finding the perimeter of a triangle?
4. What are the properties of odd integers?
5. How would the problem change if the sides were consecutive even integers?

**Tip:** Remember, the perimeter of a triangle is simply the sum of all its sides, which is useful for solving problems involving unknown side lengths.

The lengths of the three sides of a triangle (in inches) are consecutive odd integers. If the perimeter is 63 inches, find the value of the shortest of the three side lengths.

Learn how to find the shortest side of a triangle when the sides are consecutive odd integers and the perimeter is 63 inches. This algebra problem is suitable for students in Grades 6-8 and covers key concepts like triangle perimeter and consecutive odd integers.

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