Longer Side of Scalene Triangle given Semi Perimeter and other Sides Calculator

Formula Used:

\[ \text{Longer Side of Scalene Triangle} = 2 \times \text{Semiperimeter of Scalene Triangle} - (\text{Medium Side of Scalene Triangle} + \text{Shorter Side of Scalene Triangle}) \]

Semiperimeter of Scalene Triangle:

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Longer Side of Scalene Triangle:

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1. What is the Longer Side of Scalene Triangle?

The longer side of a scalene triangle is the side opposite to the largest angle in the triangle. In a scalene triangle, all three sides have different lengths, and the longer side is the one with the maximum length among them.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Longer Side} = 2 \times \text{Semiperimeter} - (\text{Medium Side} + \text{Shorter Side}) \]

Where:

Semiperimeter - Half of the total perimeter of the triangle
Medium Side - The second longest side of the triangle
Shorter Side - The shortest side of the triangle

Explanation: This formula is derived from the perimeter relationship of a triangle, where the sum of all three sides equals twice the semiperimeter.

3. Importance of Calculating the Longer Side

Details: Determining the longer side is crucial in triangle geometry for various applications including construction, engineering design, and solving complex geometric problems where side lengths affect angle calculations and area determination.

4. Using the Calculator

Tips: Enter the semiperimeter, medium side, and shorter side values in meters. All values must be positive numbers. The calculator will compute the longer side using the given formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle is a triangle with all three sides of different lengths and all three angles of different measures.

Q2: How is semiperimeter different from perimeter?
A: Semiperimeter is half of the perimeter. If perimeter is P, then semiperimeter s = P/2.

Q3: Can this formula be used for other types of triangles?
A: Yes, this formula works for all types of triangles (scalene, isosceles, equilateral) as it's based on the fundamental perimeter relationship.

Q4: What if I get a negative result?
A: A negative result indicates that the input values don't form a valid triangle. The sum of any two sides must be greater than the third side.

Q5: How accurate are the calculations?
A: The calculator provides results with up to 4 decimal places, making it suitable for most practical applications in geometry and engineering.