Question

Write an application that reads three nonzero values entered by the user and determines and prints whether they could represent the sides of a triangle.

Short answer

To decide if three values can be triangle sides, use the Triangle Inequality Theorem, which requires the sum of any two sides to be greater than the third. Check this for all three combinations of entered sides.

Step-by-step solution

Understanding the Triangle Inequality Theorem

To determine if three nonzero values can form a triangle, we check the Triangle Inequality Theorem. It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This needs to be true for all three combinations of sides.

Prompt User for Input

Create an input prompt for the user to enter three nonzero values. Label the inputs as side A, side B, and side C. Ensure that these values are positive numbers and preferably convert them into a numerical data type suitable for comparison.

Validate the Input

Check if the input values are nonzero. If any of the entered sides is zero or a negative number, print a message that the values are not valid for triangle sides and prompt the user to re-enter the values.

Apply the Triangle Inequality Theorem

Using the values entered for sides A, B, and C, check the following three conditions: A + B > C, A + C > B, and B + C > A. Each condition must be true for the values to represent the sides of a triangle.

Determine and Print the Result

If all three conditions from the Triangle Inequality Theorem are met, print a message to the user that the values can represent the sides of a triangle. Otherwise, print a message that the values cannot form a triangle.

Key concepts

Java Programming and Triangle Inequality

Java programming is a versatile and widely used language that's perfect for creating applications like the one to determine if given side lengths can form a triangle. To bring this triangle-checking application to life, you leverage Java's syntax and logic building capabilities. Java's strong type system ensures that each variable, such as the sides of a potential triangle, is declared with a specific type, which in this context would ideally be a numeric type such as an int or a double.

The logic required to verify the Triangle Inequality Theorem is implemented using methods and conditional statements within the program. Java methods, such as one that takes three parameters to represent the sides, can encapsulate the checking logic for reusability and clarity. In the example provided, the method would calculate whether the sum of any two sides is greater than the third side, ensuring the logic aligns with mathematical principles.

Conditional Statements

Conditional statements are the foundation of decision making in Java. Within our triangle-validating program, an 'if-else' statement is employed to compare the side lengths.

Consider the following pseudo-code:if (A + B > C && A + C > B && B + C > A) { // sides can form a triangle} else { // sides cannot form a triangle}
The '&&' operator is used here to ensure that each part of the Triangle Inequality Theorem is verified consecutively. If all the conditions are true, the 'if' branch executes, otherwise we fall back to the 'else' branch. These conditional checks comprise the core logic of the application and are a perfect demonstration of how powerful and essential conditional statements are in programming.

User Input Validation

Validating user input is critical to ensure an application functions correctly and efficiently. In the context of our Java application, we must validate that the users input three nonzero positive values because negative values or zero do not make sense for triangle sides.

To validate input, we use a combination of conditional logic and loops. For example, we could use a 'while' loop that continues to prompt the user until valid input is received:
while (sideA <= 0 || sideB <= 0 || sideC <= 0) { // Prompt the user to enter the three values again}
Ensuring that the input aligns with the requirements of the Triangle Inequality Theorem not only makes our program robust but also user-friendly. It prevents unnecessary errors and confusion by guiding the user to correct their inputs immediately.