Chapter 2 The Baudhāyana-Pythagoras Theorem (Class 8 - Latest Maths NCERT (Ganita Prakash II) Solutions)
Looking for the most accurate and easy-to-follow NCERT Solutions for Chapter 2: The Baudhāyana-Pythagoras Theorem? You’ve arrived at the perfect destination! This page provides clear, step-by-step guidance for the latest Class 8 Maths curriculum, exploring the fundamental relationship between the sides of a right-angled triangle. We help you bridge the gap between ancient wisdom from the Baudhāyana’s Śulba-Sūtras and modern geometry, ensuring you master the elegant relationship $a^2 + b^2 = c^2$ with complete clarity.
Our solutions offer detailed breakdowns for the Geometry of Right Triangles, identifying the hypotenuse and legs with precision. We provide thorough explanations for Irrational Numbers like $\sqrt{2}$, helping you understand why these values cannot be written as simple fractions. Whether you are identifying Baudhāyana Triples (like 3, 4, 5) or distinguishing between Primitive and Scaled versions, our guides break down every calculation. We even provide context for higher mathematical puzzles like Fermat’s Last Theorem, making complex concepts accessible.
From solving ancient problems found in Bhāskarāchārya’s Līlāvatī to mastering algebraic derivations, these resources are designed to help you excel. Curated by learningspot.co, these Ganita Prakash II solutions include visual proofs, step-by-step problem-solving methods, and historical insights. Designed for the latest CBSE syllabus, our materials ensure you build the geometric mastery needed to solve real-world problems—from architectural construction to depth calculations—with absolute confidence.
| Content On This Page | ||
|---|---|---|
| Figure It Out (Page No. 39 - 40) | Figure It Out (Page No. 47) | Figure It Out (Page No. 50) |
| Figure It Out (Page No. 52 - 54) | ||
Figure It Out (Page No. 39 - 40)
Question 1. Earlier, we saw a method to create a square with double the area of a given square paper. There is another method to do this in which two identical square papers are cut in the following way.
Can you arrange these pieces to create a square with double the area of either square?
Answer:
Question 2. The length of the two equal sides of an isosceles right triangle is given. Find the length of the hypotenuse. Find bounds on the length of the hypotenuse such that they have at least one digit after the decimal point.
(i) $3$
(ii) $4$
(iii) $6$
(iv) $8$
(v) $9$
Answer:
Question 3. The hypotenuse of an isosceles right triangle is $10$. What are its other two sidelengths?
[Hint: Find the area of the square composed of two such right triangles.]
Answer:
Figure It Out (Page No. 47)
Question 1. If a right-angled triangle has shorter sides of lengths $5$ cm and $12$ cm, then what is the length of its hypotenuse? First draw the right-angled triangle with these sidelengths and measure the hypotenuse, then check your answer using Baudhāyana’s Theorem.
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Question 2. If a right-angled triangle has a short side of length $8$ cm and hypotenuse of length $17$ cm, what is the length of the third side? Again, try drawing the triangle and measuring, and then check your answer using Baudhāyana’s Theorem.
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Question 3. Using the constructions you have now seen, how would you construct a square whose area is triple the area of a given square? Five times the area of a given square? (Baudhāyana’s Śulba-Sūtra, Verse $1.10$)
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Question 4. Let $a, b$ and $c$ denote the length of the sides of a right triangle, with $c$ being the length of the hypotenuse. Find the missing sidelength in each of the following cases:
(i) $a = 5, b = 7$
(ii) $a = 8, b = 12$
(iii) $a = 9, c = 15$
(iv) $a = 7, b = 12$
(v) $a = 1.5, b = 3.5$
Answer:
Figure It Out (Page No. 50)
Question 1. Find $5$ more Baudhāyana triples using this idea.
Answer:
Question 2. Does this method yield non-primitive Baudhāyana triples?
[Hint: Observe that among the triples generated, one of the smaller sidelengths is one less than the hypotenuse.]
Answer:
Question 3. Are there primitive triples that cannot be obtained through this method? If yes, give examples.
Answer:
Figure It Out (Page No. 52 - 54)
Question 1. Find the diagonal of a square with sidelength $5$ cm.
Answer:
Question 2. Find the missing sidelengths in the following right triangles:
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Question 3. Find the sidelength of a rhombus whose diagonals are of length $24$ units and $70$ units.
Answer:
Question 4. Is the hypotenuse the longest side of a right triangle? Justify your answer.
Answer:
Question 5. True or False — Every Baudhāyana triple is either a primitive triple or a scaled version of a primitive triple.
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Question 6. Give $5$ examples of rectangles whose sidelengths and diagonals are all integers.
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Question 7. Construct a square whose area is equal to the difference of the areas of squares of sidelengths $5$ units and $7$ units.
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Question 8. (i) Using the dots of a grid as the vertices, can you create a square that has an area of (a) $2$ sq. units, (b) $3$ sq. units, (c) $4$ sq. units, and (d) $5$ sq. unit?
(ii) Suppose the grid extends indefinitely. What are the possible integer-valued areas of squares you can create in this manner?
Answer:
Question 9. Find the area of an equilateral triangle with sidelength $6$ units.
[Hint: Show that an altitude bisects the opposite side. Use this to find the height.]
Answer: