The Baudhayana–Pythagoras Theorem — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 9
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 9, "The Baudhayana–Pythagoras Theorem". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams get right.
To score well in "The Baudhayana–Pythagoras Theorem", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on The Baudhayana–Pythagoras Theorem, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
The Baudhayana–Pythagoras Theorem — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
In a right-angled triangle, the side opposite the right angle is called the:
A.baseB.hypotenuse✓ CorrectC.altitudeD.medianAnswer: B. hypotenuse
Explanation: The side opposite the right angle is always the longest side of the triangle, called the hypotenuse — not the base, altitude, or median, which are different named parts of a triangle.
- Q2Easy
In a right triangle with legs 3 and 4, the hypotenuse is:
A.7B.6C.5✓ CorrectD.12Answer: C. 5
Explanation: 3² + 4² = 9 + 16 = 25, and √25 = 5, so the hypotenuse is 5 — not 7, which comes from simply adding the legs (3 + 4) instead of squaring them first.
- Q3Easy
Which of these is a Pythagorean triple?
A.3, 4, 5✓ CorrectB.2, 3, 4C.1, 2, 3D.4, 5, 6Answer: A. 3, 4, 5
Explanation: 3² + 4² = 9 + 16 = 25 = 5², so (3, 4, 5) satisfies the theorem exactly; none of the other listed sets of numbers square-and-add to a matching perfect square.
- Q4Easy
The diagonal of a square of side 1 unit has length:
A.2B.1C.√2✓ CorrectD.√3Answer: C. √2
Explanation: By the theorem, the diagonal is √(1² + 1²) = √2 ≈ 1.41 — not 2, which comes from adding the sides directly instead of applying the theorem.
- Q5Easy
The Baudhāyana–Pythagoras theorem is a relationship between the sides of a:
A.right-angled triangle✓ CorrectB.equilateral triangleC.circleD.squareAnswer: A. right-angled triangle
Explanation: The theorem a² + b² = c² is a relationship among the three sides of a right-angled triangle only, where c is the side opposite the 90° angle — it does not apply to equilateral triangles, circles, or squares.
- Q6Easy
In a right triangle with legs 6 and 8, the hypotenuse is:
A.14B.12C.10✓ CorrectD.48Answer: C. 10
Explanation: 6² + 8² = 36 + 64 = 100, and √100 = 10, so the hypotenuse is 10 — not 14, the sum of the legs (6 + 8), since the theorem requires squaring, not adding directly.
- Q7Medium
Find the hypotenuse of a right triangle with legs 9 and 12.
A.15✓ CorrectB.18C.13D.21Answer: A. 15
Explanation: 9² + 12² = 81 + 144 = 225, and √225 = 15, so the hypotenuse is 15 — not 21, the sum of the legs (9 + 12) rather than the square root of their squared sum.
- Q8Medium
The diagonal of a rectangle 3 cm by 4 cm is:
A.7 cmB.12 cmC.5 cm✓ CorrectD.25 cmAnswer: C. 5 cm
Explanation: The diagonal is √(3² + 4²) = √25 = 5 cm — not 7 cm, the sum of the sides (3 + 4), and not 12 cm, their product; the theorem needs squares, not simple arithmetic.
- Q9Medium
Find the hypotenuse of a right triangle with legs 20 and 15.
A.28B.23C.25✓ CorrectD.35Answer: C. 25
Explanation: 20² + 15² = 400 + 225 = 625, and √625 = 25, so the hypotenuse is 25 — not 35, which comes from adding the legs (20 + 15) instead of applying the theorem.
- Q10Medium
The diagonal of a square of side 5 cm is:
A.5√2 cm✓ CorrectB.10 cmC.25 cmD.5 cmAnswer: A. 5√2 cm
Explanation: A square's diagonal equals side × √2, so it is 5 × √2 = 5√2 cm — not 10 cm, which would be double the side rather than √2 times it.
- Q11Medium
Find the hypotenuse of a right triangle with legs 24 and 10.
A.29B.24C.34D.26✓ CorrectAnswer: D. 26
Explanation: 24² + 10² = 576 + 100 = 676, and √676 = 26, so the hypotenuse is 26 — not 34, the sum of the legs (24 + 10) rather than the theorem's result.
- Q12Hard
A right triangle has legs 6 and 8. The area of the square drawn on its hypotenuse is:
A.64B.36C.100✓ CorrectD.48Answer: C. 100
Explanation: The hypotenuse is √(6² + 8²) = √100 = 10, so the square drawn on it has area 10² = 100 — matching 6² + 8² = 36 + 64 = 100, exactly as the theorem predicts.
- Q13Hard
A right triangle has legs 1 and 2. Its hypotenuse is:
A.√5✓ CorrectB.3C.√3D.5Answer: A. √5
Explanation: Hypotenuse = √(1² + 2²) = √(1 + 4) = √5 — since 5 is not a perfect square, the answer stays as √5 rather than simplifying to a whole number like 3.
- Q14Hard
Which of these is NOT a Pythagorean triple?
A.6, 8, 12✓ CorrectB.6, 8, 10C.5, 12, 13D.8, 15, 17Answer: A. 6, 8, 12
Explanation: 6² + 8² = 36 + 64 = 100, but 12² = 144, so (6, 8, 12) fails the theorem — unlike (6, 8, 10), (5, 12, 13) and (8, 15, 17), which all satisfy a² + b² = c².
Key concepts: The Baudhayana–Pythagoras Theorem (Class 8 Mathematics)
This chapter builds the Baudhāyana–Pythagoras theorem, one of the oldest results in geometry. In any right-angled triangle the square on the hypotenuse (the side opposite the right angle) equals the sum of the squares on the other two sides: a² + b² = c². You use it to find a missing side, to recognise Pythagorean triples like (3, 4, 5) and (5, 12, 13), and to solve real problems about diagonals, ladders and distances — as well as Baudhāyana's idea that a square's diagonal builds a square of double the area.
- Right-angled triangle
- A triangle with one 90° angle. The side opposite that angle is the hypotenuse, and it is always the longest side.
- Baudhāyana–Pythagoras theorem
- In a right-angled triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse — the square on the hypotenuse equals the sum of the squares on the legs.
- Finding the hypotenuse
- When both legs are known, the hypotenuse is c = √(a² + b²); for legs 6 and 8 the hypotenuse is √100 = 10.
- Finding a leg
- When the hypotenuse and one leg are known, the other leg is √(c² − b²) — you subtract before taking the root.
- Pythagorean triple
- Three whole numbers a, b, c with a² + b² = c², such as (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
- Scaling a triple
- Any whole-number multiple of a triple is again a triple, so (6, 8, 10) and (9, 12, 15) come from (3, 4, 5).
- Converse of the theorem
- If a² + b² = c² holds for the longest side c, the triangle must be right-angled — a quick test for a right angle.
- Diagonal of a rectangle or square
- A diagonal makes a right triangle with the sides, so a rectangle's diagonal is √(l² + b²) and a square's diagonal is side × √2.
- Isosceles right triangle
- With two equal legs the hypotenuse is leg × √2; this is why a unit square has a diagonal of √2.
- Doubling a square
- Baudhāyana observed that the diagonal of a square is the side of a square with exactly twice the area.
- Applications
- The theorem measures anything modelled by a right triangle: ladders against walls, straight-line distances, and diagonal braces.
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Start this chapter free →The Baudhayana–Pythagoras Theorem — FAQs
What are the key concepts in Class 8 Mathematics The Baudhayana–Pythagoras Theorem?+
This chapter builds the Baudhāyana–Pythagoras theorem, one of the oldest results in geometry. In any right-angled triangle the square on the hypotenuse (the side opposite the right angle) equals the sum of the squares on the other two sides: a² + b² = c². You use it to find a missing side, to recognise Pythagorean triples like (3, 4, 5) and (5, 12, 13), and to solve real problems about diagonals, ladders and distances — as well as Baudhāyana's idea that a square's diagonal builds a square of double the area. Key ideas include Right-angled triangle, Baudhāyana–Pythagoras theorem, Finding the hypotenuse, Finding a leg, Pythagorean triple, Scaling a triple.
What does Class 8 Mathematics Chapter 9 (The Baudhayana–Pythagoras Theorem) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "The Baudhayana–Pythagoras Theorem": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams.
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Yes. Sign in with Google to practise "The Baudhayana–Pythagoras Theorem" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 8 till 31 March; on 1 April your account moves up to Class 9 and the rest of your year carries over. No chapter is charged separately.
How should I revise "The Baudhayana–Pythagoras Theorem" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "The Baudhayana–Pythagoras Theorem" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "The Baudhayana–Pythagoras Theorem" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from The Baudhayana–Pythagoras Theorem (Class 8 Mathematics)?+
The questions that matter most test Right-angled triangle, Baudhāyana–Pythagoras theorem, Finding the hypotenuse, Finding a leg, Pythagorean triple, Scaling a triple. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 72 questions on the chapter as timed quizzes.
Is there an online quiz for The Baudhayana–Pythagoras Theorem?+
Yes — Class 8 Mathematics The Baudhayana–Pythagoras Theorem has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.