Question

What is the maximum possible area of a rectangle whose diagonal is 5 units long?

Answer 1

area of a rectangle is given by length×breadth.

diagonal will be

$\sqrt{ {length}^{2} + {breadth}^{2} }$

given that diagonal is 5 units long.

we can write

$\sqrt{ {length}^{2} + {breadth}^{2} } = 5$

$length = \sqrt{25 - {breadth}^{2} }$

area=length×breadth

$area = breadth \times \sqrt{25 - {breadth}^{2} }$

to find the maximum area, we have to find where the above expression of area in terms of breadth is maximum.

we differentiate the expression.

the value of breadth at which the differentiation of the expression becomes zero is the maximum

(note:breadth cannot be zero or negative)