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A parallelogram is cut by two sets of m lines parallel to its sides. The number to parallelogram thus formed is :
- a)(mC2)2
- b)(m+1C2)2
- c)(m+2C2)2
- d)none
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A parallelogram is cut by two sets of m lines parallel to its sides. T...
We have the total number of horizontal lines as m + 2 and verticle lines as m + 2 also.
and we take 2 line from both side to make a parallelogram so number of ways =
and we take 2 line from both side to make a parallelogram so number of ways =
Most Upvoted Answer
A parallelogram is cut by two sets of m lines parallel to its sides. T...
Explanation:
Given:
A parallelogram is cut by two sets of m lines parallel to its sides.
To find:
The number of parallelograms formed by these cuts.
Solution:
Number of parallelograms formed by one set of lines:
When one set of lines is cut parallel to the sides of the parallelogram, it forms (m + 1) parallelograms.
Number of parallelograms formed by two sets of lines:
When two sets of lines are cut parallel to the sides of the parallelogram, each set will form (m + 1) parallelograms.
So, total parallelograms formed = (m + 1) x (m + 1) = (m + 1)^2
Combination formula:
The number of ways to choose r items from n items is given by nCr = n! / r!(n-r)!
Final Answer:
The number of parallelograms formed by cutting a parallelogram with two sets of m lines parallel to its sides is (m + 1)^2 = (m + 2)C2 = (m + 2)! / 2!(m + 2 - 2)! = (m + 2)(m + 1) / 2 = (m + 2)(m + 1) / 2 = (m + 2)C2.
Therefore, the correct answer is option C - (m + 2)C2.
Given:
A parallelogram is cut by two sets of m lines parallel to its sides.
To find:
The number of parallelograms formed by these cuts.
Solution:
Number of parallelograms formed by one set of lines:
When one set of lines is cut parallel to the sides of the parallelogram, it forms (m + 1) parallelograms.
Number of parallelograms formed by two sets of lines:
When two sets of lines are cut parallel to the sides of the parallelogram, each set will form (m + 1) parallelograms.
So, total parallelograms formed = (m + 1) x (m + 1) = (m + 1)^2
Combination formula:
The number of ways to choose r items from n items is given by nCr = n! / r!(n-r)!
Final Answer:
The number of parallelograms formed by cutting a parallelogram with two sets of m lines parallel to its sides is (m + 1)^2 = (m + 2)C2 = (m + 2)! / 2!(m + 2 - 2)! = (m + 2)(m + 1) / 2 = (m + 2)(m + 1) / 2 = (m + 2)C2.
Therefore, the correct answer is option C - (m + 2)C2.
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Community Answer
A parallelogram is cut by two sets of m lines parallel to its sides. T...
We have the total number of horizontal lines as m + 2 and verticle lines as m + 2 also.
and we take 2 line from both side to make a parallelogram so number of ways =
and we take 2 line from both side to make a parallelogram so number of ways =
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