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DIRECTIONS for questions: Select the correct alternative from the given choices.
A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?
- a)√2 : 1
- b)√3 : 1
- c)2 : 1
- d)√5 : 1
Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the giv...
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As EF is parallel to GH, △AEF and △AGH are similar. As the area of each part is equal, let area of △AEF be x. Then area of △AGH = 4x
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DIRECTIONS for questions: Select the correct alternative from the giv...
Given:
A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals.
To find:
The ratio of the length of the longest line segment to that of the shortest.
Solution:
To solve this problem, let's consider a parallelogram ABCD and draw line segments parallel to diagonal AC. Let's label the points where these line segments intersect the sides of the parallelogram as E1, E2, E3, E4, E5, E6, E7, E8, and E9.
Key Observation:
The line segments divide the parallelogram into nine regions of equal area. Therefore, the ratio of the areas of these regions will be equal to 1:1:1:1:1:1:1:1:1.
Explanation:
1. Let's denote the length of the diagonal AC as 'd'.
2. The area of the parallelogram ABCD can be calculated as the product of the base and the height. Since the base is 'd' and the height is the length of the shortest line segment (let's call it 'h'), the area of the parallelogram ABCD is given by A1 = d * h.
3. Since the areas of the nine regions are equal, the area of each region is A2 = A1/9 = (d * h)/9.
4. Now, let's consider the longest line segment, which intersects the sides of the parallelogram at points E1 and E9. Let's denote the length of this line segment as 'L'.
5. The area of the parallelogram E1E9CD can be calculated as the product of the base and the height. Since the base is 'd' and the height is 'L', the area of the parallelogram E1E9CD is A3 = d * L.
6. Since the areas of the nine regions are equal, the area of each region is A4 = A3/9 = (d * L)/9.
7. Since the areas of all the regions are equal, we can equate A2 and A4: (d * h)/9 = (d * L)/9.
8. Canceling out the common factor of (d/9), we get: h = L.
9. Therefore, the ratio of the length of the longest line segment to that of the shortest is L/h = 1/1 = 2/2 = 2:2 = 2:1.
Conclusion:
The ratio of the length of the longest line segment to that of the shortest is 2:1. Therefore, the correct option is (C) 2:1.
A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals.
To find:
The ratio of the length of the longest line segment to that of the shortest.
Solution:
To solve this problem, let's consider a parallelogram ABCD and draw line segments parallel to diagonal AC. Let's label the points where these line segments intersect the sides of the parallelogram as E1, E2, E3, E4, E5, E6, E7, E8, and E9.
Key Observation:
The line segments divide the parallelogram into nine regions of equal area. Therefore, the ratio of the areas of these regions will be equal to 1:1:1:1:1:1:1:1:1.
Explanation:
1. Let's denote the length of the diagonal AC as 'd'.
2. The area of the parallelogram ABCD can be calculated as the product of the base and the height. Since the base is 'd' and the height is the length of the shortest line segment (let's call it 'h'), the area of the parallelogram ABCD is given by A1 = d * h.
3. Since the areas of the nine regions are equal, the area of each region is A2 = A1/9 = (d * h)/9.
4. Now, let's consider the longest line segment, which intersects the sides of the parallelogram at points E1 and E9. Let's denote the length of this line segment as 'L'.
5. The area of the parallelogram E1E9CD can be calculated as the product of the base and the height. Since the base is 'd' and the height is 'L', the area of the parallelogram E1E9CD is A3 = d * L.
6. Since the areas of the nine regions are equal, the area of each region is A4 = A3/9 = (d * L)/9.
7. Since the areas of all the regions are equal, we can equate A2 and A4: (d * h)/9 = (d * L)/9.
8. Canceling out the common factor of (d/9), we get: h = L.
9. Therefore, the ratio of the length of the longest line segment to that of the shortest is L/h = 1/1 = 2/2 = 2:2 = 2:1.
Conclusion:
The ratio of the length of the longest line segment to that of the shortest is 2:1. Therefore, the correct option is (C) 2:1.
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DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer?.
DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer?.
Solutions for DIRECTIONS for questions: Select the correct alternative from the given choices. A parallelogram is divided into nine regions of equal area by drawing line segments parallel to one of its diagonals. What is the ratio of the length of the longest of the line segments to that of the shortest?a) √2 : 1b) √3 : 1c) 2 : 1d) √5 : 1Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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