Question

Prove that of all the parallelograms of which the sides are given, the parallelogram

Answer 1

Answer:

the sides of the parallelogram are equal

Answer 2

Correct Question :

Prove that all of all parallelograms of which the sides are given, the parallelogram which is rectangle has the greatest area.

AnswEr:

Let ABCD be a parallelogram in which AB = a and AD = b. Let h be the altitude corresponding ro the base AB. Then,

$\qquad \tt \: ar( {ll}^{gm} \: abcd) = ab \times h = ah$

• Since the sides a and b are given. Therefore, with the same sides a and b we can construct infinitely many parallelogram with different heights.

Now,

$\qquad \sf \: ar( {ll}^{gm} \: abcd) = ah$

$\implies \sf \: ar( {ll}^{gm} \: abcd)$

is maximum or greatest when h is maximum.

But the maximum value which h can attain is AD = b and this is possible when AD is perpendicular to AB i.e. the llgm ABCD becomes a rectangle.

#BAL

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