Important Questions and Answers for Class 8 Maths Chapter 2 The Baudhayana-Pythagoras Theorem 2025-26

1. Multiple choice questions.

1. What is the area of the square formed on the diagonal of a square of side 1 unit?

• (a) 1 sq. unit
• (b) 2 sq. units
• (c) 3 sq. units
• (d) 4 sq. units

Answer: (b) 2 sq. units

2. If the shorter sides of a right-angled triangle have lengths 3 units and 4 units, what is the length of the hypotenuse?

• (a) 5 units
• (b) 6 units
• (c) 7 units
• (d) 8 units

Answer: (a) 5 units

3. Which of the following is not a Baudhāyana triple?

• (a) (3, 4, 5)
• (b) (6, 8, 10)
• (c) (5, 11, 13)
• (d) (12, 16, 20)

Answer: (c) (5, 11, 13)

2. Very Short Answer (VSA).

1. State the Baudhāyana-Pythagoras theorem.

Answer: In a right-angled triangle with sides $a, b, c$ (where $c$ is the hypotenuse), the theorem states that $a^2 + b^2 = c^2$.

2. What is the decimal value of $\sqrt{2}$ up to three decimal places?

Answer: The value of $\sqrt{2}$ up to three decimal places is 1.414.

3. Give one example of a primitive Baudhāyana (Pythagorean) triple.

Answer: (3, 4, 5) is an example of a primitive Baudhāyana triple.

3. Short Answer Questions.

1. A square of side 1 unit is given. Using geometry, show that its diagonal forms a square of double the area. Explain why the triangles involved are congruent.

Answer: The square's diagonal length is $\sqrt{2}$ units. A square built on this diagonal has area $(\sqrt{2})^2 = 2$ sq. units, double the original. Both squares are dissected into congruent right-angled triangles by drawing horizontal and vertical lines, making the number of triangles in the larger square exactly double.

2. How can you obtain all Baudhāyana triples from a single primitive triple? Illustrate with an example.

Answer: By multiplying a primitive triple by any positive integer $k$, you get more triples: $(ka, kb, kc)$. For example, multiplying (3, 4, 5) by 3 yields (9, 12, 15), which is also a Baudhāyana triple as $9^2 + 12^2 = 15^2$.

3. A lotus stem sticks out 1 unit above water and touches the water 3 units away after bending. Find the depth of the lake using the Baudhāyana theorem.

Answer: Let the depth be $x$ units. The hypotenuse is $x + 1$, the other side is $x$, and base is 3 units. By $3^2 + x^2 = (x+1)^2 \Rightarrow 9 + x^2 = x^2 + 2x + 1 \Rightarrow 9 = 2x + 1 \Rightarrow x = 4$. So, the depth is 4 units.

4. How do you construct a square whose area is half of a given square using paper folding as mentioned in the chapter?

Answer: Take a square paper and fold it such that the crease lines pass through the midpoints of all sides. The intersecting creases form a smaller tilted square (inside the larger one) whose area is exactly half the area of the original square.

5. List all Baudhāyana triples where all numbers are less than or equal to 20.

Answer: (3, 4, 5), (6, 8, 10), (9, 12, 15), and (12, 16, 20) are the Baudhāyana triples with numbers less than or equal to 20. All are multiples of (3, 4, 5).

4. True or False Questions.

1. The decimal representation of $\sqrt{2}$ terminates after a certain number of digits.

Answer: False

2. Every Baudhāyana triple can be obtained by multiplying a primitive triple by a positive integer.

Answer: True

3. The hypotenuse is always the longest side in a right-angled triangle.

Answer: True

3. Fill in the Blanks Questions.

1. In a right-angled triangle, if the side lengths are 8 cm and 15 cm, the hypotenuse is ______ cm.

Answer: 17 cm

2. The formula for the hypotenuse $c$ of an isosceles right triangle with equal sides of length $a$ is $c = $ ______.

Answer: $a\sqrt{2}$

3. If a square has side length 5 cm, its diagonal is ______ cm.

Answer: $5\sqrt{2}$ cm

Why learning the Baudhāyana-Pythagoras Theorem is important for Class 8 Maths

Understanding the Baudhāyana-Pythagoras theorem in Class 8 lays a strong foundation in geometry. With our detailed the baudhāyana pythagoras theorem class 8 solutions, students build logical thinking, making future problem-solving much easier and enjoyable.

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