IIM-B (BBA-DBE) 2024 #1 (QA) PYQs

The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

Let $\triangle ABC$ be a triangle right-angled at $B$ with $AB = BC = 18$. The area of the largest rectangle that can be inscribed in this triangle and has $B$ as one of the vertices is:

A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle?