query: Triangle of least perimeter for a given area is the equilateral.
positive_passages.docid: 17801
positive_passages.text: Isosceles triangle has the least perimeter among triangles on the same base with same area?
negative_passages.docid: 111292
negative_passages.text: Find all triangles of which perimeter and area are numerically equal
negative_passages.docid: 129161
negative_passages.text: The minimum perimeter and maximum height of a triangle under constraints
negative_passages.docid: 61344
negative_passages.text: How to relate areas of circle, square, rectangle and triangle if they have same perimeter??
negative_passages.docid: 111042
negative_passages.text: A geometry problem from high school Olympiad selection round
negative_passages.docid: 155423
negative_passages.text: lower triangle inequality for complex numbers
negative_passages.docid: 35629
negative_passages.text: Trisect a quadrilateral into a $9$-grid; the middle has $1/9$ the area
negative_passages.docid: 56320
negative_passages.text: Prove that the circumradius of $\triangle PAB$ is constant
negative_passages.docid: 53499
negative_passages.text: Equilateral triangle inscribed in a triangle
negative_passages.docid: 145905
negative_passages.text: What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges?
negative_passages.docid: 31012
negative_passages.text: How to find the minimum perimeter oriented bounding box?
negative_passages.docid: 78464
negative_passages.text: Finding out the area of a triangle if the coordinates of the three vertices are given
negative_passages.docid: 106816
negative_passages.text: Medians of a triangle and similar triangle properties
negative_passages.docid: 26222
negative_passages.text: how can I find the Side length Two squares inside an equilateral Triangle?
negative_passages.docid: 93170
negative_passages.text: Find the side of an equilateral triangle given only the distance of an arbitrary point to its vertices
negative_passages.docid: 75657
negative_passages.text: Maximizing/Minimizing triangle area
negative_passages.docid: 116153
negative_passages.text: The Notorious Triangle Problem