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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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.
Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
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So, Reason is correct
Now, AB2 + BC2 = 242 + 102
= 576 + 49 = 625
= AC2
⇒ AB2 + BC2 = AC2
By converse of Pythagoras theorem, ∆ABC is a right angled triangle.
So, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A).
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion: In the ΔABC, AB = 24 cm, BC = 7 cm, and AC = 25 cm, then ΔABC is a right-angle triangle.
Reason: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Explanation:
To determine whether the given triangle is a right-angle triangle or not, we need to check if the square of the length of the longest side is equal to the sum of the squares of the other two sides.
Let's calculate the squares of the given sides:
AB^2 = 24^2 = 576
BC^2 = 7^2 = 49
AC^2 = 25^2 = 625
According to the Pythagorean theorem, if the sum of the squares of the two shorter sides is equal to the square of the longest side, then the triangle is a right-angle triangle.
In this case, AB^2 + BC^2 = 576 + 49 = 625 = AC^2.
Therefore, the given triangle satisfies the Pythagorean theorem and is a right-angle triangle.
Now let's analyze the reason provided in the question:
The reason states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
This reason is not directly related to determining whether a triangle is a right-angle triangle or not. It is a general property of similar triangles.
Conclusion:
The given assertion is true as the triangle satisfies the Pythagorean theorem. However, the reason provided is not the correct explanation for the given assertion. Therefore, option B is the correct answer.
Reason: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Explanation:
To determine whether the given triangle is a right-angle triangle or not, we need to check if the square of the length of the longest side is equal to the sum of the squares of the other two sides.
Let's calculate the squares of the given sides:
AB^2 = 24^2 = 576
BC^2 = 7^2 = 49
AC^2 = 25^2 = 625
According to the Pythagorean theorem, if the sum of the squares of the two shorter sides is equal to the square of the longest side, then the triangle is a right-angle triangle.
In this case, AB^2 + BC^2 = 576 + 49 = 625 = AC^2.
Therefore, the given triangle satisfies the Pythagorean theorem and is a right-angle triangle.
Now let's analyze the reason provided in the question:
The reason states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
This reason is not directly related to determining whether a triangle is a right-angle triangle or not. It is a general property of similar triangles.
Conclusion:
The given assertion is true as the triangle satisfies the Pythagorean theorem. However, the reason provided is not the correct explanation for the given assertion. Therefore, option B is the correct 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. 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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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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 : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding 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 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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