# NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 17

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Question 25:

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum when the angle between them is

Let ABC be a triangle with

Also,

Let

Also area of

Since,

For

Again differentiating w.r.t. in Eq. (v) , we get

Which is less than zero.

Hence, area of the right angled triangle is maximum, when the angle between them is