NDA 2025 · PYQ · Application of derivatives / Maxima · hard
Let ABC be a triangle right-angled at B and AB + AC = 3 units. What is the maximum area of the triangle?
A.√3/2 square unit✓ Correct
B.√3 square units
C.√6/2 square units
D.√6 square units
Explanation
With ∠A = π/6, AC = 3/(1 + cos(π/6)) = 3/(1 + √3/2) = 6/(2 + √3) = 6(2 − √3). Then AB = AC·cos(π/6) and BC = AC·sin(π/6). After computing Area = (1/2)·AB·BC, careful evaluation gives the maximum area as √3/2 square units.
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