Maharashtra Board Solutions Class 7-Maths (Practice Set 49): Chapter 13- Pythagoras Theorem

Class 7: Maths Chapter 13 solutions. Complete Class 7 Maths Chapter 13 Notes.

Maharashtra Board Solutions Class 7-Maths (Practice Set 49): Chapter 13- Pythagoras Theorem

Maharashtra Board 7th Maths Chapter 13, Class 7 Maths Chapter 13 solutions

Question 1.
Find the Pythagorean triplets from among the following sets of numbers:
i. 3,4,5
ii. 2,4,5
iii. 4,5,6
iv. 2,6,7
v. 9,40,41
vi. 4,7,8
Solution:
i. 3² = 9,4² = 16, 5² = 25
Now, 9 + 16 = 25
∴ 3² + 42 = 5²
∴ 3, 4 and 5 is a Pythagorean triplet.

ii. 2² = 4, 4² = 16, 5² = 25
But, 4 + 16 ≠ 25
∴ 2² + 4² ≠ 5²
∴ 2, 4 and 5 is not a Pythagorean triplet.

iii. 4² = 16, 5² = 25, 6² = 36
But 16 + 25 ≠ 36
∴ 4² + 5² ≠ 6²
∴ 4, 5 and 6 is not a Pythagorean triplet.

iv. 2² = 4, 6² = 36, 7² = 49
But, 4 + 36 ≠ 49
∴ 2² + 6² ≠ 7²
∴ 2, 6 and 7 is not a Pythagorean triplet.

v. 9² = 81, 40² = 1600,41² = 1681
Now, 81 + 1600 = 1681
∴ 9² + 40² = 41²
∴ 9,40 and 41 is a Pythagorean triplet.

vi. 4² = 16, 7² = 49, 8² = 64
But, 16 + 49 ≠ 64
∴ 4² + 7² ≠ 8²
∴ 4, 7 and 8 is not a Pythagorean triplet.

Question 2.
The sides of some triangles are given below. Find out which ones are right-angled triangles?
i. 8,15,17
ii. 11,12,15
iii. 11,60,61
iv. 1.5, 1.6, 1.7
v. 40, 20, 30
Solution:
i. 8² = 64, 15² = 225, 17² = 289
Now, 64 + 225 = 289
∴ 8² + 15² = 17²
The above expression is of the from (hypotenuse)² = (base)² + (height)²
∴ The sides of lengths 8,15,17 will form a right-angled triangle.

ii. 11² = 121, 12² = 144, 15² = 225
But, 121 + 144 ≠ 225
∴ 11² + 12² ≠ 25²
∴ The above expression is not of the from
(hypotenuse)² = (base)² + (height)²
∴ The sides of lengths 11, 12, 15 will not form a right-angled triangle.

iii. 11² = 121, 60² = 3600, 61² = 3721
Now, 121 +3600 = 3721
∴ 11² + 60² = 61²
∴ The above expression is of the from
(hypotenuse)² = (base)² + (height)²
∴ The sides of lengths 11, 60, 61 will form a right-angled triangle.

iv. 1.5² = 2.25, 1.6² = 2.56, 1.7² = 2.89
But, 2.25 + 2.56 ≠ 2.89
∴ 1.5² + 1.6² ≠ 1.7²
∴ The above expression is not of the from
(hypotenuse)² = (base)² + (height)²
∴ The sides of lengths 1.5, 1.6, 1.7 will not form a right-angled triangle.

v. 40² = 1600, 20² = 400, 30² = 900
But, 400 + 900 ≠ 1600
∴ 20² + 30² ≠ 40²
∴ The above expression is not of the from (hypotenuse)² = (base)² + (height)²
∴ The sides of lengths 40, 20, 30 will not form a right-angled triangle.

Intext Questions and Activities

Question 1.
From the numbers 1 to 50, pick out the Pythagorean triplets. (Textbook pg. no. 90)
Solution:

1. 3,4,5
2. 5,12,13
3. 7,24,25
4. 8,15,17
5. 9,40,41
6. 12,35,37
7. 20,21,29

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Maharashtra Board Solutions Class 7-Maths (Practice Set 49): Chapter 13- Pythagoras Theorem

Download PDF: Maharashtra Board Solutions Class 7-Maths (Practice Set 49): Chapter 13- Pythagoras Theorem PDF

Chapterwise Maharashtra Board Solutions Class 7 Maths :

• Chapter 1- Geometrical Constructions (Practice Set 1)
• Chapter 1- Geometrical Constructions (Practice Set 2)
• Chapter 1- Geometrical Constructions (Practice Set 3)
• Chapter 1- Geometrical Constructions (Practice Set 4)
• Chapter 1- Geometrical Constructions (Practice Set 5)
• Chapter 1- Geometrical Constructions (Practice Set 6)
• Chapter 1- Geometrical Constructions (Practice Set 7)
• Chapter 2- Multiplication and Division of Integers (Practice Set 8)
• Chapter 2- Multiplication and Division of Integers (Practice Set 9)
• Chapter 3- HCF and LCM (Practice Set 10)
• Chapter 3- HCF and LCM (Practice Set 11)
• Chapter 3- HCF and LCM (Practice Set 12)
• Chapter 3- HCF and LCM (Practice Set 13)
• Chapter 3- HCF and LCM (Practice Set 14)
• Chapter 4- Angles and Pairs of Angles (Practice Set 15)
• Chapter 4- Angles and Pairs of Angles (Practice Set 16)
• Chapter 4- Angles and Pairs of Angles (Practice Set 17)
• Chapter 4- Angles and Pairs of Angles (Practice Set 18)
• Chapter 4- Angles and Pairs of Angles (Practice Set 19)
• Chapter 4- Angles and Pairs of Angles (Practice Set 20)
• Chapter 4- Angles and Pairs of Angles (Practice Set 21)
• Chapter 5- Operations on Rational Numbers (Practice Set 22)
• Chapter 5- Operations on Rational Numbers (Practice Set 23)
• Chapter 5- Operations on Rational Numbers (Practice Set 24)
• Chapter 5- Operations on Rational Numbers (Practice Set 25)
• Chapter 6- Indices (Practice Set 26)
• Chapter 6- Indices (Practice Set 27)
• Chapter 6- Indices (Practice Set 28)
• Chapter 6- Indices (Practice Set 29)
• Chapter 6- Indices (Practice Set 30)
• Chapter 7- Joint Bar Graph (Practice Set 31)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 32)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 33)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 34)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 35)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 36)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 37)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 38)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 39)
• Chapter 10- Bank and Simple Interest (Practice Set 40)
• Chapter 10- Bank and Simple Interest (Practice Set 41)
• Chapter 11- Circle (Practice Set 42)
• Chapter 11- Circle (Practice Set 43)
• Chapter 12- Perimeter and Area (Practice Set 44)
• Chapter 12- Perimeter and Area (Practice Set 45)
• Chapter 12- Perimeter and Area (Practice Set 46)
• Chapter 12- Perimeter and Area (Practice Set 47)
• Chapter 13- Pythagoras Theorem (Practice Set 48)
• Chapter 13- Pythagoras Theorem (Practice Set 49)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 50)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 51)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 52)
• Chapter 14- Algebraic Formulae - Expansion of Squares (Practice Set 53)
• Chapter 15- Statistics (Practice Set 54)
• Chapter 14- Statistics (Practice Set 55)