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

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FAQs

Where do I get the Maharashtra State Board Books PDF For free download?

You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.

How to Download Maharashtra State Board Books?

Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here.  You can view or download the Maharashtra State Board Books from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums.
Step 1: Visit the official website ebalbharati.in
Step 2: On the top of the screen, select “Download PDF textbooks” 
Step 3: From the “Classes” section, select your class.
Step 4: From “Medium”, select the medium suitable to you.
Step 5: All Maharashtra board books for your class will now be displayed on the right side. 
Step 6: Click on the “Download” option to download the PDF book.

Who developed the Maharashtra State board books?

As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).

How many state boards are there in Maharashtra?

The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its nine Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.

About Maharashtra State Board (MSBSHSE)

The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: महाराष्ट्र राज्य माध्यमिक आणि उच्च माध्यमिक शिक्षण मंडळ), is an autonomous and statutory body established in 1965. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.

The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC. 

The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.