Class 10 Exam > Class 10 Questions > Instead of walking along two adjacent sides o...
Start Learning for Free
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is
- a)1/2
- b)2/3
- c)1/4
- d)3/4
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Instead of walking along two adjacent sides of a rectangular field, a ...
As shown in hint, distance saved
Free Test
FREE
| Start Free Test |
Community Answer
Instead of walking along two adjacent sides of a rectangular field, a ...
Given:
- A rectangular field
- The boy took a shortcut along the diagonal
- The boy saved a distance equal to half the longer side
To Find:
The ratio of the shorter side to the longer side
Solution:
Step 1: Understanding the Problem
Let's assume the shorter side of the rectangular field is 'a' units and the longer side is 'b' units. We need to find the ratio of the shorter side to the longer side, which is a/b.
Step 2: Visualizing the Problem
To better understand the problem, let's draw a rectangular field and label its sides.
```
________ b ________
| |
a | |
| |
-------------------
```
Step 3: Analyzing the Shortcut
When the boy takes a shortcut along the diagonal, he saves a distance equal to half the longer side. This means that the length of the diagonal is equal to (b/2) units.
Step 4: Applying the Pythagorean Theorem
In a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = (b/2)^2
Step 5: Solving the Equation
Let's solve the equation to find the relationship between a and b.
Expanding the equation:
a^2 + b^2 = b^2/4
Multiplying both sides of the equation by 4:
4a^2 + 4b^2 = b^2
Subtracting b^2 from both sides of the equation:
4a^2 = -3b^2
Dividing both sides of the equation by b^2:
4(a^2/b^2) = -3
Simplifying:
a^2/b^2 = -3/4
Taking the square root of both sides:
a/b = √(-3/4)
Since the square root of a negative number is not defined in the real number system, we can conclude that the ratio a/b does not exist.
Step 6: Conclusion
Based on the analysis, it is impossible to determine the ratio of the shorter side to the longer side. Therefore, none of the given options (a, b, c, d) is the correct answer.
Note: It is important to double-check the given question and options to ensure their accuracy.
- A rectangular field
- The boy took a shortcut along the diagonal
- The boy saved a distance equal to half the longer side
To Find:
The ratio of the shorter side to the longer side
Solution:
Step 1: Understanding the Problem
Let's assume the shorter side of the rectangular field is 'a' units and the longer side is 'b' units. We need to find the ratio of the shorter side to the longer side, which is a/b.
Step 2: Visualizing the Problem
To better understand the problem, let's draw a rectangular field and label its sides.
```
________ b ________
| |
a | |
| |
-------------------
```
Step 3: Analyzing the Shortcut
When the boy takes a shortcut along the diagonal, he saves a distance equal to half the longer side. This means that the length of the diagonal is equal to (b/2) units.
Step 4: Applying the Pythagorean Theorem
In a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = (b/2)^2
Step 5: Solving the Equation
Let's solve the equation to find the relationship between a and b.
Expanding the equation:
a^2 + b^2 = b^2/4
Multiplying both sides of the equation by 4:
4a^2 + 4b^2 = b^2
Subtracting b^2 from both sides of the equation:
4a^2 = -3b^2
Dividing both sides of the equation by b^2:
4(a^2/b^2) = -3
Simplifying:
a^2/b^2 = -3/4
Taking the square root of both sides:
a/b = √(-3/4)
Since the square root of a negative number is not defined in the real number system, we can conclude that the ratio a/b does not exist.
Step 6: Conclusion
Based on the analysis, it is impossible to determine the ratio of the shorter side to the longer side. Therefore, none of the given options (a, b, c, d) is the correct answer.
Note: It is important to double-check the given question and options to ensure their accuracy.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer?
Question Description
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer?.
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer?.
Solutions for Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side isa)1/2b)2/3c)1/4d)3/4Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup