GATE EC 2014 Set 4 — Question 39
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is
Correct answer
(C) 60^
Solution
Let the hypotenuse be and the side be . Let the angle between them be .
Then and the other side is .
Given (constant).
.
The area of the triangle is .
Substitute :
.
To maximize , we differentiate with respect to and set to zero:
Using the quotient rule:
Since is an angle in a triangle, . Thus, .
Then and the other side is .
Given (constant).
.
The area of the triangle is .
Substitute :
.
To maximize , we differentiate with respect to and set to zero:
Using the quotient rule:
Since is an angle in a triangle, . Thus, .
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