# A parallelogram and a rectangle are on the same base between the same parallels. Prove that perimeter of the parallelogram is greater than that of the rectangle.

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by Krakler

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by Krakler

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The Brainliest Answer!

Hence, because of two larger sides, parallelogram has greater perimeter than rectangle.

To Prove ;Perimeter of parallelogram ABCD> perimeter of rectangle ABEF.

i.e. AB+BC+CD+AD>AB+BE+EF+AF .

proof; Since opposite side of a parallelogram and a rectangle are equal.

therefore AB=DC [ABCD IS A PARALLELOGRAM}

and AB=EF [ IS ABEF IS A RECTANGLE ]

DC=EF ..............(1)

;AB+DC=AB+EF ...............(11)

since of all the segment that can be drawn to a give line from a point not lying on it the perpendicular segment is the shortest.

;BE<BC and AF<AD

BC>BE and AD>AF

BC+AD>BE+AF .....................(111)

Adding (11) and (111), we get

AB+DC+BC+AD>AB+EF+BE+AF

AB+BC+CD+DA>AB+BE+EF+FA

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