JEE Main2013MathematicsApplication of DerivativesActual

The maximum area of a right angled triangle with hypotenuse h is :

Options

Ah^2 2 2
Bh^2 2
Ch^2 2
Dh^2 4

Correct answer

D. h^2 4

Step-by-step solution

Let base =b Altitude (or perpendicular) = h^2-b^2 Area, A = 1 2 base altitude = 1 2 b h^2-b^2 d ~A d b = 1 2 [ h^2-b^2 +b -2 b 2 h^2-b^2 ]= 1 2 [ h^2-2 b^2 h^2-b^2 ] Put d ~A d b =0, b= h 2 Maximumarea = 1 2 h 2 h^2- h^2 2 = h^2 4

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