The side AB of a triangle ABC is c. The median BD is of length k. If BDA = and < 90^, then the area of triangle ABC is Option 1: k^2 /2 + k sqrt(c^2 + k^2 ^2 ) Option 2: k^2 2/2 + k sqrt(c^2 - k^2 ^2 ) Option 3: k^2 2/2 + k sqrt(c^2 - k^2 ^2 ) Option 4: k^2 /2 + k sqrt(c^2 + k^2 ^2 )

The answer is 'k^2 2/2 + k sqrt(c^2 - k^2 ^2 )'. View full solution:

IPMAT Indore - The side AB of a triangle ABC is c. The median BD is of length k. If BDA = and < 90^, then the area of triangle ABC is | PYQs + Solutions

IPMAT Indore

Geometry

Hard

$\dfrac{k^2 \sin \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}$

$\dfrac{k^2 \sin 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}$

$\dfrac{k^2 \cos 2\theta}{2} + k \sin \theta \sqrt{c^2 - k^2 \sin^2 \theta}$

$\dfrac{k^2 \cos \theta}{2} + k \sin \theta \sqrt{c^2 + k^2 \sin^2 \theta}$

✅ Correct Option: 2