Triangle Solutions Calculator: Determine Triangle Validity

What is Triangle Validity?

Triangle validity refers to the conditions that must be met for three given lengths to form a triangle. This concept is fundamental in geometry and has practical applications in various fields, including construction and design.

The Triangle Inequality Theorem

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This must be true for all three combinations of sides.

Formula for Triangle Validity

For a triangle with sides \(a\), \(b\), and \(c\), the following inequalities must all be satisfied:

1. \(a + b > c\)
2. \(b + c > a\)
3. \(c + a > b\)

Where:

• \(a\), \(b\), and \(c\) represent the lengths of the three sides of the triangle

Calculation Steps

To determine if three lengths can form a valid triangle, follow these steps:

1. Add the lengths of the two shortest sides.
2. Compare this sum to the length of the longest side.
3. If the sum is greater than the longest side, proceed to check the other two combinations.
4. If all three inequalities are satisfied, the triangle is valid.

Example

Let's consider three lengths: 3 units, 4 units, and 5 units.

1. \(3 + 4 = 7 > 5\) (Valid)
2. \(3 + 5 = 8 > 4\) (Valid)
3. \(4 + 5 = 9 > 3\) (Valid)

Since all three inequalities are satisfied, these lengths can form a valid triangle.

Visual Representation

This diagram illustrates a valid triangle formed by sides of lengths 3, 4, and 5 units.