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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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.
Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. Can you explain this answer?
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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 not correct
So, Assertion is correct
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Direction: In the following questions, A statement of Assertion (A) i...
Assertion: The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5 cm, then the length of QR is 6 cm.
Reason: The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
To understand why option C is the correct answer, let's break down the assertion and reason given in the question.
Understanding the Assertion:
The assertion states that the areas of two similar triangles ABC and PQR are in the ratio 9:16. This means that the ratio of the areas of these triangles is 9/16.
Understanding the Reason:
The reason given states that the ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides. In other words, if two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
Explanation:
Let's assume that the lengths of the corresponding sides of the triangles ABC and PQR are in the ratio of x:y. Therefore, the ratio of the areas of these triangles will be (x^2):(y^2).
Given that the ratio of the areas of the triangles ABC and PQR is 9:16, we can write the equation as:
(x^2)/(y^2) = 9/16
To find the length of QR, we need to find the value of y. Since we are given that BC = 4.5 cm, we can set up a proportion between the corresponding sides as follows:
BC/PQ = AB/QR
4.5/y = x/y
x = 4.5
Now, substituting the value of x in the equation (x^2)/(y^2) = 9/16, we get:
(4.5^2)/(y^2) = 9/16
20.25/(y^2) = 9/16
Cross-multiplying and solving for y, we get:
16 * 20.25 = 9 * (y^2)
324 = 9 * (y^2)
y^2 = 324/9
y^2 = 36
y = 6
Therefore, the length of QR is 6 cm.
Conclusion:
From the explanation above, it is clear that the assertion and reason are both true. However, the reason does not correctly explain the assertion because it only states the general concept of the ratio of areas of similar triangles being equal to the ratio of their corresponding sides, without specifically addressing the given scenario. Hence, option C is the correct answer.
Reason: The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
To understand why option C is the correct answer, let's break down the assertion and reason given in the question.
Understanding the Assertion:
The assertion states that the areas of two similar triangles ABC and PQR are in the ratio 9:16. This means that the ratio of the areas of these triangles is 9/16.
Understanding the Reason:
The reason given states that the ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides. In other words, if two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
Explanation:
Let's assume that the lengths of the corresponding sides of the triangles ABC and PQR are in the ratio of x:y. Therefore, the ratio of the areas of these triangles will be (x^2):(y^2).
Given that the ratio of the areas of the triangles ABC and PQR is 9:16, we can write the equation as:
(x^2)/(y^2) = 9/16
To find the length of QR, we need to find the value of y. Since we are given that BC = 4.5 cm, we can set up a proportion between the corresponding sides as follows:
BC/PQ = AB/QR
4.5/y = x/y
x = 4.5
Now, substituting the value of x in the equation (x^2)/(y^2) = 9/16, we get:
(4.5^2)/(y^2) = 9/16
20.25/(y^2) = 9/16
Cross-multiplying and solving for y, we get:
16 * 20.25 = 9 * (y^2)
324 = 9 * (y^2)
y^2 = 324/9
y^2 = 36
y = 6
Therefore, the length of QR is 6 cm.
Conclusion:
From the explanation above, it is clear that the assertion and reason are both true. However, the reason does not correctly explain the assertion because it only states the general concept of the ratio of areas of similar triangles being equal to the ratio of their corresponding sides, without specifically addressing the given scenario. Hence, option C 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 : The areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. 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 areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.Reason : The ratio of the areas of two similar triangles is equal to 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 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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