NCERT Class 12-Mathematics: Chapter – 6 Application of Derivatives Part 17 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Long Answer (L. A.)

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

Answer:

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