State true or false:

All parallelograms having equal areas have the same perimeters. Observe all the four triangles FAB, EAB, DAB and CAB as shown below.

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True

False

answer is B.

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Detailed Solution

Here, we have to find whether all parallelograms that have equal areas have the same perimeters or not.
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We know that when the base of a parallelogram is multiplied with its altitude, the resulting product obtained is its area.
Next, it is possible that parallelograms with the same area may or may not be of equal perimeter.
The reason is that there may be variation in the heights and bases of the parallelograms.
Therefore, we conclude that it may be possible for a number of parallelograms to have the same area, but their perimeters can be different.
Hence, the statement is false.
Hence, the correct option is (2).

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