• The length two sides of a triangle are ‘a’ and ‘b’
• Angle between the sides ‘a’ and ‘b’ is θ.
• The area of the triangle is maximum.
Let us consider,
The area of the ΔPQR is given be
For finding the maximum/ minimum of given function, we can find it by differentiating it with θ and then equating it to zero. This is because if the function A (θ) has a maximum/minimum at a point c then A’(c) = 0.
Differentiating the equation (1) with respect to θ:
To find the critical point, we need to equate equation (2) to zero.
Cos θ = 0
Now to check if this critical point will determine the maximum area, we need to check with second differential which needs to be negative.
Consider differentiating the equation (2) with θ :
Now let us find the value of
As , so the function A is maximum at
As the area of the triangle is maximum when
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