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Question

Choose the correct statements from the following:

Statement 1: All the parallelograms having the same base and lying between the same parallels have equal areas.

Statement 2: All the parallelograms having the same base and lying between the same parallels have same perimeters.

Statement 3: Of all the parallelograms having same base and lying between same parallels, rectangle will have the smallest perimeter.

Statement 4: All the parallelograms having equal areas must have the same base but they may or may not lie between the same parallels.



A

1, 2, 4

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B

1, 2

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C

1, 2, 3, 4

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D

1, 2, 3

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Solution

The correct option is A

1, 2


Statement 1: All the parallelograms having the same base and lying between the same parallels have equal areas.

Reason: This is because base is same and height is also same since they are between same parallel lines. This makes the area (base × height) same.

Statement 2: All the parallelograms having the same base and lying between the same parallels have same perimeters.

Reason: Even though one pair of sides are of same lengths, the other pairs’ lengths vary. Thus the parallelograms having the same base and lying between the same parallels have different perimeters.

Statement 3: Of all the parallelograms having same base and lying between same parallels, rectangle will have the smallest perimeter.

Reason: The rectangle will have the smallest perimeter of all. Try to think and figure it out.

Statement 4: All the parallelograms having equal areas must have the same base but they may or may not lie between the same parallels.

Reason: Two parallelograms having equal areas may be such that base and height of one is equal to height and base of another respectively. They may have different bases and may lie between same or different parallel lines.


Mathematics

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