Proove  that  of  all  parallelograms  of  given  perimeter , the  rectangle  has  the  same  area.

Asked by Nithya Anna Binu | 4th Feb, 2014, 09:46: PM

Expert Answer:

I hope the question is
 
all parallelograms with given perimeter, rectangle has maximum area.

begin mathsize 12px style A r e a space o f space p a r a l l e log r a m space A space equals space l cross times b cross times sin space theta i f space w e space d i f f e r e n t i a t e space w i t h space theta comma space fraction numerator d A over denominator d theta end fraction space equals space l cross times b cross times cos space theta sin c e space p e r i m e t e r space i s space f i x e d comma space l space a n d space b space r e m a i n s space c o n s tan t. t o space m a x i m i z e space A comma space w e space e q u a t e fraction numerator d A over denominator d theta end fraction space equals space 0 space a n d space g e t space t h e space v a l u e space f o r space theta fraction numerator d A over denominator d theta end fraction space equals space 0 comma space i f space theta space equals space pi over 2 i f space theta space equals space pi over 2 comma space p a r a l l e log r a m space i s space r e c tan g l e. space end style

Answered by Thiyagarajan K | 8th Jan, 2018, 08:08: PM

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