Question

In the given figure, ABCD and ABEF are parallelograms. If ar(ΔACD) =50 cm^2, then the ar(ΔBGE) eequal??​

Answer 1

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Given that ABEF is a rectangle and ABCD is a parallelogram, with the same base AB and have equal areas.

Since ∥gm & rectangle have equal areas with same base AB, thereore it will be between same set of ∥al lines.

AB=CD⟶(1)  [opposite sides of the ∥gm]

AB=EF⟶(2)  [opposite sides of rectangle]

from (1) & (2), we get

CD=EF⟶(3)

In △ADF,

∠AFD=900

AD>AF  [∵  Hypotenuse is greater than other sides.]  ⟶(4)

BC>BE  [Since BC=AD and BE=AF]  ⟶(5)

Perimeter of ∥gm ABCD =AB+BC+CD+DA

                                             =AB+BC+EF+DA      [from equation (3)]

                                             >EF+FA+AB+BE       [Using (5)]

which is the perimeter of rectangle ABEF.

Therefore perimeter of ∥gm with the same base and with equal areas is greater than the perimeter of the rectangle.

∴  Perimeter ABCD > Perimeter ABEF