UPSC Exam > UPSC Questions > There are 4 horizontal and 4 vertical lines, ...
Start Learning for Free
There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?
- a)16
- b)24
- c)36
- d)42
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
There are 4 horizontal and 4 vertical lines, parallel and equidistant ...
4 vertical and 4 horizontal lines
Squares are: a, b, c, d, e, f, g, h, i, (abde), (bcef), (degh), (efhi), ABCD
Rectangles are: (ab), (bc), (de), (ef), (gh), (hi), (ad), (dg), (be), (eh), (cf), (fi),
(abc), (def), (ghi), (adg), (beh), (cfi),
(abcdef), (defghi), (adgbeh), (behcfi)
Required number = 14 + 22 = 36
Squares are: a, b, c, d, e, f, g, h, i, (abde), (bcef), (degh), (efhi), ABCD
Rectangles are: (ab), (bc), (de), (ef), (gh), (hi), (ad), (dg), (be), (eh), (cf), (fi),
(abc), (def), (ghi), (adg), (beh), (cfi),
(abcdef), (defghi), (adgbeh), (behcfi)
Required number = 14 + 22 = 36
Most Upvoted Answer
There are 4 horizontal and 4 vertical lines, parallel and equidistant ...
Maximum number of rectangles and squares that can be formed on a board with 4 horizontal and 4 vertical lines can be calculated as follows:
Rectangles:
- We can choose any two horizontal lines out of 4 in 4C2 ways i.e. 6 ways.
- Similarly, we can choose any two vertical lines out of 4 in 4C2 ways i.e. 6 ways.
- The total number of rectangles formed by these two horizontal and two vertical lines is 6 x 6 = 36.
Squares:
- We can choose any two horizontal lines out of 4 in 4C2 ways i.e. 6 ways.
- Similarly, we can choose any two vertical lines out of 4 in 4C2 ways i.e. 6 ways.
- Out of these 6 x 6 = 36 rectangles, we need to count only those which are squares.
- A square is formed when the distance between two horizontal lines is equal to the distance between two vertical lines.
- Since there are 4 horizontal and 4 vertical lines, there are 3 distances for each i.e. 3 horizontal distances and 3 vertical distances.
- Out of these 3 horizontal distances, only one distance is equal to each of the 3 vertical distances.
- Therefore, there are only 3 squares that can be formed by these 4 horizontal and 4 vertical lines.
- Hence, the total number of squares formed is 3.
Therefore, the maximum number of rectangles and squares that can be formed is 36 + 3 = 39, which is option C.
Rectangles:
- We can choose any two horizontal lines out of 4 in 4C2 ways i.e. 6 ways.
- Similarly, we can choose any two vertical lines out of 4 in 4C2 ways i.e. 6 ways.
- The total number of rectangles formed by these two horizontal and two vertical lines is 6 x 6 = 36.
Squares:
- We can choose any two horizontal lines out of 4 in 4C2 ways i.e. 6 ways.
- Similarly, we can choose any two vertical lines out of 4 in 4C2 ways i.e. 6 ways.
- Out of these 6 x 6 = 36 rectangles, we need to count only those which are squares.
- A square is formed when the distance between two horizontal lines is equal to the distance between two vertical lines.
- Since there are 4 horizontal and 4 vertical lines, there are 3 distances for each i.e. 3 horizontal distances and 3 vertical distances.
- Out of these 3 horizontal distances, only one distance is equal to each of the 3 vertical distances.
- Therefore, there are only 3 squares that can be formed by these 4 horizontal and 4 vertical lines.
- Hence, the total number of squares formed is 3.
Therefore, the maximum number of rectangles and squares that can be formed is 36 + 3 = 39, which is option C.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer?
Question Description
There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer?.
There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer?.
Solutions for There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer?, a detailed solution for There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?a)16b)24c)36d)42Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup