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

Explanation

"Given: A parallelogram ABCD whose sides are given.

To prove: The area of the parallelogram ABCD is the greatest when it is a rectangle.

Cons.: Draw `DEbotAB`.

Proof : Area of parallelogram ABCD = Base x corresponding altitude = `ABxxDE`

When parallelogram ABCD is a rectangle, then its area is ABxxDA ( `angle DAB=90^*`)

In right `triangle` DEA,

`angle DEA>angle DAE`

`DA>DE`

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