Chapter 8.3, Problem 1E

To determine

To write: a program for Pythagorean triples, what did it list, and which of these are primitive Pythagorean triples.

Answer to Problem 1E

Pythagorean triples describes the three integer side is the lengths of a right triangle and list them.

The primitive Pythagorean triples with hypotenuse less than or equal to 10: $\left(3,4,5\right),\left(5,12,13\right),\left(7,24,25\right),\left(8,15,17\right)$ .

Explanation of Solution

Concept used:Use different syntax that is used to PRINT, FOR LOOP, IF condition and do other operations to print Pythagorean triples, while running the program.

A Pythagorean triples are the three positive integers $\mathrm{a},\mathrm{b},\text{ and }\mathrm{c}$ , such that ${\mathrm{a}}^2+{\mathrm{b}}^2={\mathrm{c}}^2$ . It says that the three integer side is the lengths of a right triangle. Where $\mathrm{a}$ is perpendicular, $\mathrm{b}$ is base, $\text{and }\mathrm{c}$ is the hypotenuse. Here we are assuming the length (hypotenuse) will be less than or equal to 10 and using Pythagoras Theorem.

program to print the Pythagorean triples:

10 CLC

20 INT $\mathrm{a},\mathrm{b}$ ;

30 FLOAT $\mathrm{c}$ ;

40 FOR $\mathrm{a}=1;\mathrm{a}<=10;\mathrm{a}++$

50 FOR $\mathrm{b}=1;\mathrm{b}<=10;\mathrm{b}++$

60  $\mathrm{c}=\mathrm{s}\mathrm{q}\mathrm{r}\mathrm{t}\left(\mathrm{a}*\mathrm{a}+\mathrm{b}*\mathrm{b}\right)$ ;

70 IF $\mathrm{c}==\left(\mathrm{I}\mathrm{N}\mathrm{T}\right)\mathrm{c}$ ;

80 PRINT “The Pythagorean triples are:”, $\mathrm{a},\mathrm{b},\left(\mathrm{I}\mathrm{N}\mathrm{T}\right)\mathrm{c}$ ;

90 END

Here line 20 enters only integer numbers and line 30 enters float value. Line 40 and 50 runs the values of $\mathrm{a},\text{ and }\mathrm{b}$ till 10, because it is restricted to 10. Line 70 checks whether the obtained value is an integer or not. Line 80 prints the Pythagorean triples. Line 90 comes out from the program after reaching $\mathrm{a},\text{ and }\mathrm{b}$ to 10.

Output:

The Pythagorean triples are:

  $\begin{array}{l}\left(3,4,5\right)\\ \left(4,3,5\right)\\ \left(5,12,13\right)\\ \left(6,8,10\right)\\ \left(7,24,25\right)\\ \left(8,15,17\right)\\ \left(9,12,15\right)\\ \left(10,24,26\right)\end{array}$

Conclusion:

It describes the three integer side is the lengths of a right triangle.

The primitive Pythagorean triples with hypotenuse less than or equal to 10: $\left(3,4,5\right),\left(5,12,13\right),\left(7,24,25\right),\left(8,15,17\right)$ .