A question related to quadrilaterals

[Yashwanth]

Consider the family R of parallelograms on equal bases whose areas are equal. Prove that , in R rectangle has the least perimeter.

 

[Yashwanth]

I want to know how to approach these questions

 

[Deleted member 4993]

Consider the family R of parallelograms on equal bases whose areas are equal. Prove that , in R rectangle has the least perimeter.

Assume that;

the length of the "equal" side of the parallelograms is "E".

the length of the "variable" side of the parallelograms is "V"

The "non-obtuse" angle between E and V is "t"

What would be the area of the parallelogram as a function of E, V and t? Call that A.

Now express V as a function of E, t and A. Please show us your work ......

 

[Dr.Peterson]

Consider the family R of parallelograms on equal bases whose areas are equal. Prove that , in R rectangle has the least perimeter.

You could do this in many ways, which is one reason we ask you to show some thoughts of your own, or at least tell us what you are learning. You could do this with trigonometry, with coordinates, with vectors, with algebra, with calculus, or just with synthetic geometry. Take your pick!