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
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
AD > EG
Hence, ar(rectangle ABCD) > ar (parallelogram ABFE)
Answered by | 17th Aug, 2017, 02:23: PM
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