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Q.

State true or false.


Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Then the perimeter of the parallelogram is greater than that of the rectangle.


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a

True

b

False 

answer is A.

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Detailed Solution

Given;
A Parallelogram = ABCD  A rectangle = ABEF                    [are on same base and have equal areas]
Opposite side of parallelogram
AB = CD    Opposite side of rectangle    AB = EF  and
F=E=90
As, hypotenuse of right angle > other sides. So,
AD>AF and BC>BE
Question ImageNow, we have the perimeter of ABCD
=AB+BC+CD+DA Also, perimeter of ABEF
=AB+BE+EF+FA
As,
CD = EF and
AD > AF, BC > BE
Hence, the perimeter of ABCD > perimeter of ABEF.
So, the given statement is true.
Option 1 is correct.
 
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