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The Baudhayana-Pythagoras Theorem – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 9. Notes, key terms, important questions with answers and MCQs.

Chapter overview

In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. Baudhayana stated this in the Sulba Sutras long before Pythagoras.

The theorem

c² = a² + b², where c is the hypotenuse (side opposite the right angle).
Converse: if c² = a² + b², the triangle is right-angled.
Baudhayana's Sulba Sutra (around 800 BCE) gives the rule for a rectangle's diagonal.

Pythagorean triples

Whole numbers satisfying a² + b² = c²: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25).
Multiples also work: (6, 8, 10), (9, 12, 15).
For any m > 1: (2m, m² − 1, m² + 1) is a triple.

Key terms

Hypotenuse: longest side of a right triangle, opposite the right angle
Pythagorean triple: three whole numbers with a² + b² = c²
Baudhayana Sulba Sutra: ancient Indian text that stated the diagonal rule for rectangles, the same idea as Pythagoras' theorem

Formulas

c² = a² + b²
Diagonal of a rectangle = √(l² + b²)

Important questions with answers

Check whether a triangle with sides 7, 24 and 25 is right-angled.2 marks

7² + 24² = 49 + 576 = 625 = 25². Yes, it is right-angled.

A 13 m ladder reaches a window 12 m high. How far is its foot from the wall?3 marks

√(13² − 12²) = √25 = 5 m.

State the theorem and find the length of the diagonal of a rectangular field 40 m × 30 m. How much shorter is walking along the diagonal than along two sides? Also find a Pythagorean triple with 10 as the smallest number.5 marks

In a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides (Baudhayana stated it for the diagonal of a rectangle). Diagonal = √(40² + 30²) = √2500 = 50 m. Along two sides = 70 m, so the diagonal is 20 m shorter. Using (2m, m² − 1, m² + 1) with m = 5: (10, 24, 26).

Quick revision

The theorem works only for right triangles.
3-4-5 is the smallest triple.
Baudhayana gave it in the Sulba Sutras.

Exam tips

Always square the longest side for c.
Ladder and wall problems are right-triangle problems.

Practice MCQs

In a right triangle the longest side is the
1. hypotenuse
2. perpendicular
3. base
4. median
Show answer
Answer: (a) hypotenuse. Hypotenuse.
If the legs are 6 and 8, the hypotenuse is
1. 12
2. 10
3. 14
4. 9
Show answer
Answer: (b) 10. √(36 + 64).
Which is a Pythagorean triple?
1. (5, 12, 13)
2. (4, 5, 6)
3. (6, 7, 9)
4. (2, 3, 4)
Show answer
Answer: (a) (5, 12, 13). 25 + 144 = 169.
A 13 m ladder reaches 12 m up a wall. Its foot is how far from the wall?
1. 5 m
2. 1 m
3. 25 m
4. 7 m
Show answer
Answer: (a) 5 m. √(169 − 144).
A right triangle has legs 9 cm and 12 cm. The hypotenuse is
1. 15 cm
2. 13 cm
3. 21 cm
4. 17 cm
Show answer
Answer: (a) 15 cm. √(81 + 144).
A triangle has sides 9, 12 and 15. It is
1. acute
2. right-angled
3. obtuse
4. equilateral
Show answer
Answer: (b) right-angled. 81 + 144 = 225.
Diagonal of a square of side 5 cm is
1. 5√2 cm
2. 10 cm
3. 25 cm
4. 5 cm
Show answer
Answer: (a) 5√2 cm. √(25 + 25).
Which is a Pythagorean triple
1. (5, 12, 14)
2. (8, 15, 17)
3. (6, 7, 9)
4. (4, 5, 6)
Show answer
Answer: (b) (8, 15, 17). 64 + 225 = 289.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.