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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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.
Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.
- 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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Direction: In the following questions, A statement of Assertion (A) i...
Reason is true. [standard result]
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For Assertion, since ΔABC ∼ ΔDEF
(ratio of areas of two similar Δs is equal to the ratio of the squares of corresponding sides)
= 4 x 25 = 100 cm2
Assertion is true. But Reason is not correct explanation for Assertion.
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Direction: In the following questions, A statement of Assertion (A) i...
Assertion: ABC and DEF are two similar triangles such that BC = 4 cm, EF = 5 cm, and the area of ΔABC = 64 cm2. Then the area of ΔDEF = 100 cm2.
Reason: The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
Explanation:
To prove the assertion, we need to establish whether the reason given is correct or not.
Similar Triangles:
Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are in proportion.
Ratio of Area:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
So, if ABC and DEF are similar triangles, the ratio of their areas will be equal to the square of the ratio of their corresponding sides.
Let's calculate the ratio of the areas of ΔABC and ΔDEF:
Given: Area of ΔABC = 64 cm2, BC = 4 cm, and EF = 5 cm
We can calculate the ratio of their areas using the formula:
Area of ΔABC/Area of ΔDEF = (BC/EF)2
Substituting the given values:
64/Area of ΔDEF = (4/5)2
64/Area of ΔDEF = 16/25
Cross-multiplying:
25 * 64 = 16 * Area of ΔDEF
Area of ΔDEF = (25 * 64)/16
Area of ΔDEF = 100 cm2
Conclusion:
Hence, we can conclude that the area of ΔDEF is indeed 100 cm2, which proves the assertion. Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion. So, the correct answer is option B.
Reason: The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
Explanation:
To prove the assertion, we need to establish whether the reason given is correct or not.
Similar Triangles:
Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are in proportion.
Ratio of Area:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
So, if ABC and DEF are similar triangles, the ratio of their areas will be equal to the square of the ratio of their corresponding sides.
Let's calculate the ratio of the areas of ΔABC and ΔDEF:
Given: Area of ΔABC = 64 cm2, BC = 4 cm, and EF = 5 cm
We can calculate the ratio of their areas using the formula:
Area of ΔABC/Area of ΔDEF = (BC/EF)2
Substituting the given values:
64/Area of ΔDEF = (4/5)2
64/Area of ΔDEF = 16/25
Cross-multiplying:
25 * 64 = 16 * Area of ΔDEF
Area of ΔDEF = (25 * 64)/16
Area of ΔDEF = 100 cm2
Conclusion:
Hence, we can conclude that the area of ΔDEF is indeed 100 cm2, which proves the assertion. Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion. So, the correct answer is option B.
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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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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 : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.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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