Prove that of all the parallelograms of the given sides, a rectangle has the greatest area.

Asked by Topperlearning User | 17th Aug, 2017, 12:23: PM

Expert Answer:

ABCD is a rectangle and ABFE is a parallelogram, such that
AD = BC = AE = BF
Area of rectangle = base x altitude
                             = AB x AD
Area of parallelogram ABFC = base x altitude
                                                = AB x EG
In AGE, AE > EG    (AE is the hypotenuse of right triangle)
But AD = AE
Hence, ar(rectangle ABCD) > ar (parallelogram ABFE)

Answered by  | 17th Aug, 2017, 02:23: PM