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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7
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 '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 the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
View all questions of this test
So, Reason is correct
So, Assertion is correct.
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion and Reasoning:
Assertion: ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7.
Reason: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Explanation:
When two triangles are similar, their corresponding sides are in proportion. Let's assume that the corresponding sides of ΔABC and ΔDEF are AB and DE, BC and EF, and AC and DF respectively.
Now, according to the given information,
ar(ΔABC) = 36 cm^2
ar(ΔDEF) = 49 cm^2
We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Mathematically, it can be represented as:
(ar(ΔABC) / ar(ΔDEF)) = (AB^2 / DE^2) = (BC^2 / EF^2) = (AC^2 / DF^2)
Since ar(ΔABC) = 36 cm^2 and ar(ΔDEF) = 49 cm^2, we can substitute these values in the above equation:
(36 / 49) = (AB^2 / DE^2) = (BC^2 / EF^2) = (AC^2 / DF^2)
To find the ratio of the corresponding sides, we take the square root of the ratio of the areas:
√(36 / 49) = AB / DE = BC / EF = AC / DF
√(36 / 49) = AB / DE
6 / 7 = AB / DE
Therefore, the ratio of the corresponding sides AB and DE is 6 : 7.
Conclusion:
Hence, both the assertion and reason are true, and the reason is the correct explanation of the assertion.
Assertion: ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7.
Reason: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Explanation:
When two triangles are similar, their corresponding sides are in proportion. Let's assume that the corresponding sides of ΔABC and ΔDEF are AB and DE, BC and EF, and AC and DF respectively.
Now, according to the given information,
ar(ΔABC) = 36 cm^2
ar(ΔDEF) = 49 cm^2
We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Mathematically, it can be represented as:
(ar(ΔABC) / ar(ΔDEF)) = (AB^2 / DE^2) = (BC^2 / EF^2) = (AC^2 / DF^2)
Since ar(ΔABC) = 36 cm^2 and ar(ΔDEF) = 49 cm^2, we can substitute these values in the above equation:
(36 / 49) = (AB^2 / DE^2) = (BC^2 / EF^2) = (AC^2 / DF^2)
To find the ratio of the corresponding sides, we take the square root of the ratio of the areas:
√(36 / 49) = AB / DE = BC / EF = AC / DF
√(36 / 49) = AB / DE
6 / 7 = AB / DE
Therefore, the ratio of the corresponding sides AB and DE is 6 : 7.
Conclusion:
Hence, both the assertion and reason are true, and the reason is the correct explanation of the assertion.
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
|
|
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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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 : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7Reason : 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 '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