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In the given figure, if parallelogram $ABCD$ and rectangle ABFE are of equal area, then find the relation of their perimeters.

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Perimeter

A B C D <

perimeter ABFE

Perimeter

A B C D >

perimeter ABFE

Perimeter

A B C D =

perimeter ABFE

None of the above

answer is B.

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Detailed Solution

Given, a parallelogram ABCD and rectangle ABEF having equal area and has same base.
Question Image

Now In

Δ A E D

And

Δ B F C

A E = B F [Opposite sides of parallelogram] A D = B C [Opposite sides of parallelogram] ∠ A E D = ∠ B F C [Both are right angles .]

Thus,

Δ A E D ≅ Δ B F C

. [By SAS test]

∴ D E = F C

[CPCT]
Again

Δ A E D

is a right angle.
So, AD is the hypotenuse

A D > A E

Now, from the figure we can say that,

F E = F D + D E

D C = D F + F C ⇒ D C = F D + D E (as DE=FC) ⇒ D C = E F

[

∵ D E = F C

]
Since AD>AE, perimeter

A B C D >

perimeter ABFE.
Hence, the correct option is 2.

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In the given figure, if parallelogram ABCD and rectangle ABFE are of equal area, then find the relation of their perimeters.

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In the given figure, if parallelogram $ABCD$ and rectangle ABFE are of equal area, then find the relation of their perimeters.