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

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

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Text solutionVerified

Solution: ABCD is a parallelogram
So, AB=CD and AC=BD
ABEF is a rectangle
So, AB=EF and AE=BF
Perimeter ABCD= 2(AB+AC)
Perimeter ABEF= 2(AB+AE)
It can be easily seen that AC>AE
So, Perimeter of parallelogram is more than rectangle.

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Question Text	Parallelogram ABCD and rectangle ABEF are on the same base AB and have equalareas. Show that the perimeter of the parallelogram is greater than that of the rectangle.
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

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