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Question

If two sides of a triangle are given, then the area of the triangle will be maximum if the angle between the given sides be.


A

π3

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B

π4

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C

π6

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D

π2

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Solution

The correct option is D

π2


Explanation for the correct answer:

Find the angle between the given sides:

Let a and b be given sides, then the area,

A=12absinC

Differentiate the above area with respect to C.

dAdC=12abdsinCdC=12abcosC[dsinxdx=cosx]

A is the maximum, when dAdC=0

12abcosC=0cosC=0C=90°[cos90°=0]=π2

Hence, the correct option is D


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