Class 10 Exam > Class 10 Questions > Direction: In the following questions, A sta...
Start Learning for Free
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cm
Reason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Direction: In the following questions, A statement of Assertion (A) i...
We know that In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is Pythagoras theorem. So, Reason is correct
View all questions of this test
Let the side of square be x cm.
In ∆ABD, by Pythagoras theorem, we have BD2 = AB2 + AD2
⇒ 162 = x2 + x2
⇒ 2x2 = 256 ⇒ x2 = 128 ⇒ x = 8√2 cm
So, Assertion is also correct.
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion: The length of the side of a square whose diagonal is 16 cm is 8√2 cm.
Reason: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Explanation:
To understand the given assertion and reason, let's consider a square with a diagonal of 16 cm.
1. Finding the length of the side of the square:
In a square, the diagonal divides the square into two congruent right triangles.
2. Applying the Pythagorean theorem:
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's consider the side of the square as 'a' cm. Then, using the Pythagorean theorem, we can write the following equation for one of the right triangles:
a^2 + a^2 = (16)^2
Simplifying the equation, we get:
2a^2 = 256
Dividing both sides by 2, we get:
a^2 = 128
Taking the square root of both sides, we get:
a = √128
Simplifying further, we get:
a = 8√2 cm
Conclusion:
From the calculations above, we can see that the length of the side of the square is indeed 8√2 cm. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion. Hence, option A is the correct answer.
Reason: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Explanation:
To understand the given assertion and reason, let's consider a square with a diagonal of 16 cm.
1. Finding the length of the side of the square:
In a square, the diagonal divides the square into two congruent right triangles.
2. Applying the Pythagorean theorem:
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's consider the side of the square as 'a' cm. Then, using the Pythagorean theorem, we can write the following equation for one of the right triangles:
a^2 + a^2 = (16)^2
Simplifying the equation, we get:
2a^2 = 256
Dividing both sides by 2, we get:
a^2 = 128
Taking the square root of both sides, we get:
a = √128
Simplifying further, we get:
a = 8√2 cm
Conclusion:
From the calculations above, we can see that the length of the side of the square is indeed 8√2 cm. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion. Hence, option A is the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
Direction: In the following questions, A statement of Assertion (A) i...
We know that In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is Pythagoras theorem. So, Reason is correct
Let the side of square be x cm.
In ∆ABD, by Pythagoras theorem, we have BD2 = AB2 + AD2
⇒ 162 = x2 + x2
⇒ 2x2 = 256 ⇒ x2 = 128 ⇒ x = 8√2 cm
So, Assertion is also correct.
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
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?
Question Description
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cmReason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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