CAT (QA) PYQs

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of triangle is

From a triangle $ABC$ with sides of lengths $40$ ft, $25$ ft and $35$ ft, a triangular portion $GBC$ is cut off where $G$ is the centroid of $ABC$. The area, in sq ft, of the remaining portion of triangle $ABC$ is

A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is