The Baudhayana-Pythagoras Theorem - Exercise 2.3 Class 8 Maths - Chapter 2 NCERT Solutions
Class 8 Maths Ganita Prakash 2026–27 Term 2 Chapter 2, Baudhayana-Pythagoras Theorem – Exercise 2.3 detailed solutions are provided below by the ALLEN expert team to support students in understanding the questions and preparing effectively for their exams and future academic learning. The solutions follow the updated NCERT syllabus and provide clear explanations for each question.Exercise 2.3 Find more Baudhāyana triples using the given method . Why does the method always produce primitive triples ? Find some primitive Baudhāyana triples that cannot be obtained using this particular method . The exercise clearly helps the students comprehend how Baudhāyana triples are generated, what makes a triple primitive and the limits of the method given.
1.0Download Class 8 Maths Chapter 2 Ex 2.3 NCERT Solutions PDF
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2.0Detailed NCERT Solutions onTheBaudhayana-Pythagoras Theorem Exercise 2.3 Class 8 Maths (Ganita Prakash Term 2)
1. Find 5 more Baudhāyana triples using this idea.
Sol. (i) (1+3+5+…+47)+49=252
242+72=252(24,7,25)
(ii) (1+3+5+…+79)+81=412
402+92=412(40,9,41)
(iii) (1+3+5+…+119)+121=612
602+112=612(60,11,61)
(iv) (1+3+5+…+167)+169=852
842+132=852(84,13,85)
(v) (1+3+5+…+223)+225=1132
1122+152=1132(112,15,113)
- Does this method yield non-primitive Baudhāyana triples?
[Hint: Observe that among the triples generated, one of the smaller side-lengths is one less than the hypotenuse.)
Sol. No, it never yields non-primitive triples.
Let's look at the generated triplesexample (7,24,25)
- The hypotenuse (n) and one of the legs ( n−1 ) are consecutive integers (like 24 and 25).
- Consecutive integers never share a common factor other than 1 .
- Because two of the three numbers share no common factors, it is impossible for all three to share a common factor. Therefore, the triple is always primitive.
3. Are there primitive triples that cannot be obtained through this method? If yes, give examples.
Sol. Yes, there are.
The method on this page strictly produces triples where the hypotenuse is exactly 1 unit larger than one of the legs (because they are n and n−1 ).
However, there are primitive triples which don't follow this logic Example:
Some examples are (8, 15, 17), (20, 99, 101), (120, 209, 241)
Thus, not all primitive triples can be generated by this method.
3.0Key Concepts of Chapter 2 - The Baudhayana-Pythagoras Theorem Exercise 2.3
- Finding five more Baudhāyana triples using the given method.
- Understanding that the method generates triples where one shorter side is one less than the hypotenuse.
- Understanding why the triples generated by this method are always primitive.
- Identifying primitive Baudhāyana triples that cannot be obtained using the given method.
- Giving examples of primitive triples that cannot be generated by this method.
4.0Benefits of NCERT Solutions Class 8 Maths Chapter 2 Exercise 2.3
- Provides a clear method for generating new Baudhāyana triples.
- Explains why the triples generated by the given method are primitive.
- Helps identify the pattern between the hypotenuse and one of the shorter sides.
- Clarifies that not every primitive Baudhāyana triple can be obtained using this method.
- Uses examples to distinguish triples that can and cannot be generated through the given method.