IPMAT Indore 2024
Geometry
Triangles
Easy
Let be a triangle right-angled at with . The area of the largest rectangle that can be inscribed in this triangle and has as one of the vertices is:
Let be a triangle right-angled at with . The area of the largest rectangle that can be inscribed in this triangle and has as one of the vertices is:
Entered answer:
✅ Correct Answer: 81
Let's place on a coordinate system with at the origin .Since angle is , we can place at and at .
Since is one vertex of the rectangle, the other vertices will be at , , and where lies on the hypotenuse .The equation of line is .
Let's find the area of the rectangle:Area = To maximize the area, we take the derivative and set it equal to zero:When ,
The rectangle has vertices at , , , and Maximum area = square units.
Since is one vertex of the rectangle, the other vertices will be at , , and where lies on the hypotenuse .The equation of line is .
Let's find the area of the rectangle:Area = To maximize the area, we take the derivative and set it equal to zero:When ,
The rectangle has vertices at , , , and Maximum area = square units.
Related questions:
IPMAT Indore 2019
IPMAT Indore 2020