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A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?
- a)91 m
- b)77 m
- c)143 m
- d)195 m
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A rectangle with integer sides has perimeter 300 m and area less than...
To solve this problem, we need to find a rectangle with integer sides, a perimeter of 300 m, and an area less than 5000 sq. m.
Let's assume the length of the rectangle is L and the breadth is B.
Perimeter of the rectangle = 2(L + B) = 300 m
Area of the rectangle = L * B
From the given information, we know that L > B.
We are also given that the rectangle can be divided into 7, 11, or 13 equal parts, and the area of each part is an integer.
Let's consider the case where the rectangle can be divided into 7 equal parts:
- Area of each part = (L * B) / 7
Since the area of each part needs to be an integer, L * B must be divisible by 7. This means either L or B should be divisible by 7.
Also, the area of the rectangle needs to be less than 5000 sq. m. So, we can set an upper limit for L:
L * B < />
L < 5000="" />
Now, let's consider the case where the rectangle can be divided into 11 equal parts:
- Area of each part = (L * B) / 11
Similar to the previous case, either L or B should be divisible by 11.
Again, the area of the rectangle needs to be less than 5000 sq. m:
L * B < />
L < 5000="" />
Finally, let's consider the case where the rectangle can be divided into 13 equal parts:
- Area of each part = (L * B) / 13
Either L or B should be divisible by 13.
And the area of the rectangle needs to be less than 5000 sq. m:
L * B < />
L < 5000="" />
We can now combine all the conditions and constraints:
- L and B are integers
- L > B
- L + B = 150 (from perimeter equation)
- L * B < />
By analyzing the possible values of L and B, we find that the length of the rectangle is 143 m (option C).
Let's assume the length of the rectangle is L and the breadth is B.
Perimeter of the rectangle = 2(L + B) = 300 m
Area of the rectangle = L * B
From the given information, we know that L > B.
We are also given that the rectangle can be divided into 7, 11, or 13 equal parts, and the area of each part is an integer.
Let's consider the case where the rectangle can be divided into 7 equal parts:
- Area of each part = (L * B) / 7
Since the area of each part needs to be an integer, L * B must be divisible by 7. This means either L or B should be divisible by 7.
Also, the area of the rectangle needs to be less than 5000 sq. m. So, we can set an upper limit for L:
L * B < />
L < 5000="" />
Now, let's consider the case where the rectangle can be divided into 11 equal parts:
- Area of each part = (L * B) / 11
Similar to the previous case, either L or B should be divisible by 11.
Again, the area of the rectangle needs to be less than 5000 sq. m:
L * B < />
L < 5000="" />
Finally, let's consider the case where the rectangle can be divided into 13 equal parts:
- Area of each part = (L * B) / 13
Either L or B should be divisible by 13.
And the area of the rectangle needs to be less than 5000 sq. m:
L * B < />
L < 5000="" />
We can now combine all the conditions and constraints:
- L and B are integers
- L > B
- L + B = 150 (from perimeter equation)
- L * B < />
By analyzing the possible values of L and B, we find that the length of the rectangle is 143 m (option C).
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Community Answer
A rectangle with integer sides has perimeter 300 m and area less than...
T + b = 150 --- (1)
The area has to be a multiple of 7, 11 and 13 and not any other prime numbers- So these are the only factors of the areas.
t x b = 1001 = 7 x 11 x 13
The different possibilities are:
For equation [1] to be satisfied-t=143 and b=7
Hence, [3]
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A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer?
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A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect 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 A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect 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 A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer?.
A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect 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 A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect 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 A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect 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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A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A rectangle with integer sides has perimeter 300 m and area less than 5000 sq. m. The rectangle can be divided into any of 7 or 11 or 13 parts (each part having equal areas in each case) such that the area of each part is again an integer (in sq. meter). Also, the rectangle cannot be divided into any other number of parts that are prime (other than 7, 11 and 13) such that all parts have equal area and also the area being an integer. If the length of the rectangle is greater than its breadth, then what is the length of rectangle?a)91 mb)77 mc)143 md)195 mCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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