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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?
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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
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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.
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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.
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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?
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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.
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