The Baudhayana Pythagoras Theorem — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "The Baudhayana Pythagoras Theorem" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "The Baudhayana Pythagoras Theorem" — 8 important questions with detailed answers fo…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 8 Mathematics — The Baudhayana Pythagoras Theorem. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
The Baudhayana Pythagoras Theorem — All 8 Questions Solved
Q1. If the sides of a right triangle are 3 cm and 4 cm, find the hypotenuse.
Step 1: Use Pythagoras theorem: c² = a² + b²
Step 2: Given a = 3 cm, b = 4 cm
Step 3: c² = 3² + 4² = 9 + 16 = 25
Step 4: c = √25 = 5 cm
Step 5: The hypotenuse is 5 cm
Q2. Check if a triangle with sides 5, 12, and 13 is a right triangle.
Step 1: For a right triangle, the longest side is the hypotenuse.
Step 2: Hypotenuse = 13, other sides = 5 and 12
Step 3: Check: 5² + 12² = 25 + 144 = 169
Step 4: Also, 13² = 169
Step 5: Since 5² + 12² = 13², it is a right triangle (Pythagorean triple)
Q3. Find the hypotenuse of a right triangle with legs 6 m and 8 m.
Step 1: Use Pythagoras theorem: c² = a² + b²
Step 2: Given a = 6 m, b = 8 m
Step 3: c² = 6² + 8² = 36 + 64 = 100
Step 4: c = √100 = 10 m
Step 5: The hypotenuse is 10 m
Q4. In a right triangle, if hypotenuse = 13 cm and one leg = 5 cm, find the other leg.
Step 1: Use Pythagoras theorem: c² = a² + b²
Step 2: Given c = 13 cm, a = 5 cm, find b
Step 3: 13² = 5² + b²
Step 4: 169 = 25 + b²
Step 5: b² = 169 − 25 = 144
Step 6: b = √144 = 12 cm
Q5. Verify if 7, 24, 25 form a Pythagorean triple.
Step 1: Check if 7² + 24² = 25²
Step 2: 7² = 49, 24² = 576, 25² = 625
Step 3: 49 + 576 = 625
Step 4: Since 7² + 24² = 25², it is a Pythagorean triple
Q6. A ladder of length 13 m is placed against a wall. The foot of the ladder is 5 m from the wall. How high does the ladder reach on the wall?
Step 1: The ladder, wall, and ground form a right triangle.
Step 2: Hypotenuse (ladder) = 13 m, base (distance from wall) = 5 m
Step 3: Use Pythagoras theorem: 13² = 5² + h²
Step 4: 169 = 25 + h²
Step 5: h² = 169 − 25 = 144
Step 6: h = √144 = 12 m
Step 7: The ladder reaches 12 m high on the wall
Q7. Find the hypotenuse of a right triangle with legs 9 cm and 12 cm.
Step 1: Use Pythagoras theorem: c² = a² + b²
Step 2: Given a = 9 cm, b = 12 cm
Step 3: c² = 9² + 12² = 81 + 144 = 225
Step 4: c = √225 = 15 cm
Step 5: The hypotenuse is 15 cm
Q8. Is a triangle with sides 8, 15, and 17 a right triangle?
Step 1: Check if it satisfies Pythagoras theorem.
Step 2: 8² + 15² = 64 + 225 = 289
Step 3: 17² = 289
Step 4: Since 8² + 15² = 17², it is a right triangle
The Baudhayana Pythagoras Theorem — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. In a right-angled triangle, if 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse, which of the following statements is true according to the Baudhayana-Pythagoras Theorem?
- A. a + b = c
- B. a² - b² = c²
- C. a² + b² = c²
- D. a + b = c²
Answer: C. a² + b² = c² — The Baudhayana-Pythagoras Theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
MCQ 2. Which side of a right-angled triangle is always the longest?
- A. The side opposite to the acute angle
- B. The side adjacent to the right angle
- C. The hypotenuse
- D. One of the legs
Answer: C. The hypotenuse — The hypotenuse is the side opposite to the right angle and is always the longest side in a right-angled triangle.
MCQ 3. A right-angled triangle has legs of length 6 cm and 8 cm. What is the length of its hypotenuse?
- A. 10 cm
- B. 14 cm
- C. √28 cm
- D. √100 cm
Answer: A. 10 cm — Using the Baudhayana-Pythagoras Theorem, Hypotenuse² = Leg1² + Leg2² = 6² + 8² = 36 + 64 = 100. So, Hypotenuse = √100 = 10 cm.
MCQ 4. If the hypotenuse of a right-angled triangle is 13 cm and one of its legs is 5 cm, what is the length of the other leg?
- A. 8 cm
- B. 12 cm
- C. 144 cm
- D. 18 cm
Answer: B. 12 cm — Let the unknown leg be 'x'. According to the theorem, 5² + x² = 13². So, 25 + x² = 169, which means x² = 169 - 25 = 144. Therefore, x = √144 = 12 cm.
MCQ 5. Which of the following sets of side lengths can form a right-angled triangle?
- A. 2 cm, 3 cm, 4 cm
- B. 3 cm, 4 cm, 5 cm
- C. 4 cm, 5 cm, 6 cm
- D. 5 cm, 6 cm, 7 cm
Answer: B. 3 cm, 4 cm, 5 cm — For a right-angled triangle, the sum of squares of the two smaller sides must equal the square of the largest side. For 3, 4, 5: 3² + 4² = 9 + 16 = 25, and 5² = 25. Since 25 = 25, it forms a right-angled triangle.
MCQ 6. Baudhayana's Sulbasutra, an ancient Indian text, contains early statements of which important mathematical theorem?
- A. Fundamental Theorem of Algebra
- B. Pythagoras Theorem
- C. Binomial Theorem
- D. Euclidean Algorithm
Answer: B. Pythagoras Theorem — The Baudhayana Sulbasutra is an ancient Indian text that contains one of the earliest statements of what is now known as the Pythagoras Theorem, predating Pythagoras himself.
MCQ 7. In a right-angled triangle PQR, if angle Q is 90 degrees, which side is the hypotenuse?
- A. PQ
- B. QR
- C. PR
- D. Cannot be determined
Answer: C. PR — The hypotenuse is the side opposite to the right angle. If angle Q is 90 degrees, then side PR is opposite to angle Q, making it the hypotenuse.
MCQ 8. The Baudhayana-Pythagoras Theorem applies only to which type of triangle?
- A. Equilateral triangles
- B. Isosceles triangles
- C. Scalene triangles
- D. Right-angled triangles
Answer: D. Right-angled triangles — The Baudhayana-Pythagoras Theorem specifically states the relationship between the sides of a right-angled triangle.
MCQ 9. What are the two sides forming the right angle in a right-angled triangle called?
- A. Hypotenuses
- B. Diagonals
- C. Altitudes
- D. Legs
Answer: D. Legs — The two sides that form the right angle in a right-angled triangle are called the legs (or sometimes cathetus).
MCQ 10. If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, what kind of triangle is it?
- A. Acute-angled triangle
- B. Obtuse-angled triangle
- C. Right-angled triangle
- D. Equilateral triangle
Answer: C. Right-angled triangle — This is the converse of the Baudhayana-Pythagoras Theorem. If a² + b² = c², then the triangle is a right-angled triangle.
MCQ 11. A ladder 17 meters long rests against a vertical wall. If the foot of the ladder is 8 meters away from the base of the wall, how high up the wall does the ladder reach?
- A. 9 meters
- B. 15 meters
- C. 16 meters
- D. 25 meters
Answer: B. 15 meters — The ladder, wall, and ground form a right-angled triangle. Hypotenuse = 17m, one leg = 8m. Let the height be 'h'. So, h² + 8² = 17². h² + 64 = 289. h² = 225. h = √225 = 15 meters.
MCQ 12. A rectangle has a length of 24 cm and a width of 10 cm. What is the length of its diagonal?
- A. 26 cm
- B. 34 cm
- C. √676 cm
- D. Both A and C
Answer: D. Both A and C — The diagonal of a rectangle forms a right-angled triangle with two adjacent sides. Diagonal² = Length² + Width² = 24² + 10² = 576 + 100 = 676. So, Diagonal = √676 = 26 cm. Both A and C are correct, as √676 is 26 cm.
MCQ 13. Which of the following is a Pythagorean triplet?
- A. (4, 5, 6)
- B. (6, 8, 10)
- C. (7, 8, 9)
- D. (9, 10, 11)
Answer: B. (6, 8, 10) — A Pythagorean triplet (a, b, c) satisfies a² + b² = c². For (6, 8, 10): 6² + 8² = 36 + 64 = 100, and 10² = 100. Thus, 100 = 100.
MCQ 14. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, what is the distance between their tops?
- A. 13 m
- B. 15 m
- C. 17 m
- D. 18 m
Answer: A. 13 m — Draw a horizontal line from the top of the shorter pole to the taller pole. This forms a right-angled triangle. The height difference is 11-6 = 5m (one leg), and the distance between feet is 12m (other leg). The distance between tops is the hypotenuse. Hypotenuse² = 5² + 12² = 25 + 144 = 169. Hypotenuse = √169 = 13 m.
MCQ 15. The perimeter of a right-angled triangle is 30 cm. If its hypotenuse is 13 cm, what are the lengths of its other two sides?
- A. 5 cm, 12 cm
- B. 6 cm, 11 cm
- C. 7 cm, 10 cm
- D. 8 cm, 9 cm
Answer: A. 5 cm, 12 cm — Let the other two sides be 'a' and 'b'. We know a + b + 13 = 30, so a + b = 17. Also, a² + b² = 13² = 169. By checking options or solving system: If a=5, b=12, then 5+12=17 (correct) and 5²+12² = 25+144 = 169 (correct).
MCQ 16. If the sides of a triangle are x, 15, and 17, and it is a right-angled triangle, what is the value of x?
- A. 6
- B. 7
- C. 8
- D. 9
Answer: C. 8 — Since 17 is the largest side, it must be the hypotenuse. So, x² + 15² = 17². x² + 225 = 289. x² = 289 - 225 = 64. Therefore, x = √64 = 8.
MCQ 17. A boat travels 9 km east and then 12 km north. How far is the boat from its starting point?
- A. 15 km
- B. 21 km
- C. √135 km
- D. 18 km
Answer: A. 15 km — The eastward and northward movements form the legs of a right-angled triangle, and the distance from the starting point is the hypotenuse. Distance² = 9² + 12² = 81 + 144 = 225. Distance = √225 = 15 km.
MCQ 18. The diagonals of a rhombus are 16 cm and 30 cm. What is the length of each side of the rhombus?
- A. 17 cm
- B. 20 cm
- C. 24 cm
- D. 34 cm
Answer: A. 17 cm — The diagonals of a rhombus bisect each other at right angles. This forms four right-angled triangles with legs equal to half the diagonals (16/2 = 8 cm and 30/2 = 15 cm). The side of the rhombus is the hypotenuse. Side² = 8² + 15² = 64 + 225 = 289. Side = √289 = 17 cm.
MCQ 19. The length of the sides of a right-angled triangle are consecutive integers. What are the lengths of the sides?
- A. 3, 4, 5
- B. 4, 5, 6
- C. 5, 6, 7
- D. 6, 7, 8
Answer: A. 3, 4, 5 — Let the sides be x, x+1, x+2. For a right-angled triangle, x² + (x+1)² = (x+2)². Testing 3,4,5: 3²+4² = 9+16=25 and 5²=25. This is the only Pythagorean triplet with consecutive integers.
MCQ 20. In an isosceles right-angled triangle, if the length of each equal side is 7 cm, what is the length of the hypotenuse?
- A. √49 cm
- B. √98 cm
- C. 14 cm
- D. 7√2 cm
Answer: D. 7√2 cm — Let the hypotenuse be 'c'. c² = 7² + 7² = 49 + 49 = 98. So, c = √98 = √(49 × 2) = 7√2 cm.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.