Question

(Sides of a Triangle) Write a program that reads three nonzero double values and determines and prints whether they could represent the sides of a triangle.

Short answer

To determine if three values can form a triangle, verify that the sum of each pair of values is greater than the third value. If this holds for all combinations, they can form a triangle.

Step-by-step solution

Understanding Triangle Inequality Theorem

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

Input Validation

Ensure that the input comprises three nonzero double values, representing potential sides of a triangle. If any value is zero or negative, the input is invalid because a triangle side must be a positive number.

Apply the Triangle Inequality Theorem

Check the three conditions derived from the Triangle Inequality Theorem: a + b > c, a + c > b, and b + c > a, where a, b, and c are the sides of the triangle.

Determine if Values Form a Triangle

If all three conditions are met, the values can form a triangle. If any condition is not met, the values cannot form a triangle.

Print the Result

Print the output stating whether the given values can or cannot represent the sides of a triangle based on the results from the conditions checked.

Key concepts

C++ Programming

C++ programming is a skill that involves writing code in the C++ language to create software applications. When programming in C++, it's essential to understand the syntax and semantics of the language to implement logic accurately and effectively.

In the context of the exercise, a C++ program is used to determine if three given lengths can form a triangle. To accomplish this task, a programmer must write a sequence of instructions that the computer will follow. This includes taking user input, processing that input according to the Triangle Inequality Theorem, and providing the user with appropriate feedback.

The C++ program, therefore, must safely handle the input values, check them against the theorem's conditions, and print an intelligible result. Such a program not only teaches important programming concepts but also integrates mathematical reasoning with code, showcasing the power of programming in problem-solving.

Conditional Statements

Conditional statements are a fundamental component of many programming languages, including C++. They allow the program to make decisions and execute certain parts of the code based on whether a condition is true or false.

The structure of a conditional statement typically involves an 'if' keyword followed by a condition enclosed in parentheses. If the condition evaluates to true, a block of code will execute. There may also be an optional 'else' block that executes if the condition is false.

Example of an If-Else Statement

if (condition) {
// code to execute if condition is true
} else {
// code to execute if condition is false
}

When writing the program to determine if three lengths can make a triangle, conditional statements check each of the conditions of the Triangle Inequality Theorem. If all conditions are satisfied, we conclude that a triangle is possible; otherwise, we conclude it is not.

Input Validation

Input validation is the process of verifying that user input meets the expected format, type, and value range before being processed by the program. It is a critical step in programming because it helps prevent errors and enhances program stability and security.

In our triangle program scenario, input validation ensures that the user enters three nonzero and positive double values, representing potential triangle sides. This is crucial because a triangle cannot have sides with zero or negative length. By checking the input right at the start, we prevent the program from running with invalid data, which may lead to incorrect results or program crashes.

Implementing proper input validation in a C++ program can be done using conditional statements. Before applying the Triangle Inequality Theorem, it's essential to verify that each side complies with the requirements of being greater than zero. If the validation fails, the program should issue an appropriate message and halt further calculations.