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(a) Given three positive numbers x, y and z, we can determine if these are the lengths of a triangle by checking that the following inequalities hold simultaneously: z < x +y x < y + z y < z + x. Write a function which implements the above idea. Its exact declaration should be: bool is_triangle (double x, double y, double z) The function should contain no cout statements. Here are some test cases: is triangle (0,0,0) → false • is triangle(-1,1,1) → false • is triangle(1,1,10) → false • is triangle(1,10,1) → false • is triangle (1,1,1) → true • is-triangle(2,13,12) H true (b) Write a function which computes the area of a triangle given three side lengths via Heron's formula: https://en.wikipedia.org/wiki/Heron%27s_formula Assume that the side lengths form a valid triangle. Its exact declaration should be: double area(double x, double y, double z) The function should contain no cout statements. Here are some test cases: • area(1,1,1) H 0.433013 • area(2,13,12) H 10.7906 • area(12,13,2) → 10.7906 (c) Write a main function which reads three double values from the standard input. If the values are the side lengths of a triangle, the program should print: The values 3.0, 4.0 and 5.0 are the side lengths of a triangle with area 6.0. Otherwise: The values 1.1, 2.0 and 5.0 are not the side lengths of a triangle. All floating point values should be printed with 6 digits of precision. For full credit, the main function must call the functions from (a) and (b).

(a) Given three positive numbers x, y and z, we can determine if these are the lengths of a triangle by checking that the following inequalities hold simultaneously: z < x +y x < y + z y < z + x. Write a function which implements the above idea. Its exact declaration should be: bool is_triangle (double x, double y, double z) The function should contain no cout statements. Here are some test cases: is triangle (0,0,0) → false • is triangle(-1,1,1) → false • is triangle(1,1,10) → false • is triangle(1,10,1) → false • is triangle (1,1,1) → true • is-triangle(2,13,12) H true (b) Write a function which computes the area of a triangle given three side lengths via Heron's formula: https://en.wikipedia.org/wiki/Heron%27s_formula Assume that the side lengths form a valid triangle. Its exact declaration should be: double area(double x, double y, double z) The function should contain no cout statements. Here are some test cases: • area(1,1,1) H 0.433013 • area(2,13,12) H 10.7906 • area(12,13,2) → 10.7906 (c) Write a main function which reads three double values from the standard input. If the values are the side lengths of a triangle, the program should print: The values 3.0, 4.0 and 5.0 are the side lengths of a triangle with area 6.0. Otherwise: The values 1.1, 2.0 and 5.0 are not the side lengths of a triangle. All floating point values should be printed with 6 digits of precision. For full credit, the main function must call the functions from (a) and (b).

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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(a) Given three positive numbers x, y and z, we can determine if these are the lengths of a triangle by checking that the following inequalities hold simultaneously: z < x + y x < y + z y < z + x. Write a function which implements the above idea. Its exact declaration should be: bool is_triangle(double x, double y, double z) The function should contain no cout statements. Here are Some test cases: • is triangle(0,0,0) → false • is triangle(-1,1,1) → false • is triangle(1,1,10) –→ false • is triangle(1,10,1) → false is triangle (1,1,1) → true • is triangle(2,13,12) + true (b) Write a function which computes the area of a triangle given three side lengths via Heron's formula: https://en.wikipedia.org/wiki/Heron%27s_formula Assume that the side lengths form a valid triangle. Its exact declaration should be: double area(double x, double y, double z) The function should contain no cout statements. Here are some test cases: • area (1,1,1) → 0.433013 • area(2,13,12) → 10.7906 • area(12,13,2) → 10.7906 (c) Write a main function which reads three double values from the standard input. If the values are the side lengths of a triangle, the program should print: The values 3.0, 4.0 and 5.0 are the side lengths of a triangle with area 6.0. Otherwise: The values 1.1, 2.0 and 5.0 are not the side lengths of a triangle. All floating point values should be printed with 6 digits of precision. For full credit, the main function must call the functions from (a) and (b).
Transcribed Image Text:(a) Given three positive numbers x, y and z, we can determine if these are the lengths of a triangle by checking that the following inequalities hold simultaneously: z < x + y x < y + z y < z + x. Write a function which implements the above idea. Its exact declaration should be: bool is_triangle(double x, double y, double z) The function should contain no cout statements. Here are Some test cases: • is triangle(0,0,0) → false • is triangle(-1,1,1) → false • is triangle(1,1,10) –→ false • is triangle(1,10,1) → false is triangle (1,1,1) → true • is triangle(2,13,12) + true (b) Write a function which computes the area of a triangle given three side lengths via Heron's formula: https://en.wikipedia.org/wiki/Heron%27s_formula Assume that the side lengths form a valid triangle. Its exact declaration should be: double area(double x, double y, double z) The function should contain no cout statements. Here are some test cases: • area (1,1,1) → 0.433013 • area(2,13,12) → 10.7906 • area(12,13,2) → 10.7906 (c) Write a main function which reads three double values from the standard input. If the values are the side lengths of a triangle, the program should print: The values 3.0, 4.0 and 5.0 are the side lengths of a triangle with area 6.0. Otherwise: The values 1.1, 2.0 and 5.0 are not the side lengths of a triangle. All floating point values should be printed with 6 digits of precision. For full credit, the main function must call the functions from (a) and (b).
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