query: Find all triangles whose area is 1 and length of sides are all rational numbers.
positive_passages.docid: 152509
positive_passages.text: Does there exist a side-rational triangle of area $1$?
negative_passages.docid: 97473
negative_passages.text: Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$
negative_passages.docid: 77547
negative_passages.text: Find integers $a,b,c,d$ such that
negative_passages.docid: 35629
negative_passages.text: Trisect a quadrilateral into a $9$-grid; the middle has $1/9$ the area
negative_passages.docid: 136054
negative_passages.text: If $a_1,a_2,a_3,...,a_n$ are the side lengths of $A_1A_2A_3...A_n$ convex polygon,then$\frac{a^2_1+a^2_2+a^2_3+....+a^2_{n-1}}{a^2_n}$ is
negative_passages.docid: 133925
negative_passages.text: Find All Solutions to System of Congruence
negative_passages.docid: 130470
negative_passages.text: Find the angle ADE of the given triangle.
negative_passages.docid: 22241
negative_passages.text: Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$?
negative_passages.docid: 45702
negative_passages.text: For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$
negative_passages.docid: 45366
negative_passages.text: How to calculate the area of a 3D triangle?
negative_passages.docid: 101476
negative_passages.text: If $A$, $B$ and $C$ are the angles of a triangle then find the value of $\Delta$
negative_passages.docid: 17801
negative_passages.text: Isosceles triangle has the least perimeter among triangles on the same base with same area?
negative_passages.docid: 142008
negative_passages.text: Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
negative_passages.docid: 43398
negative_passages.text: Find possible number of triangles with integer sides for a given inradius
negative_passages.docid: 78407
negative_passages.text: Are there infinitely-many numbers that are both square and triangular?
negative_passages.docid: 19019
negative_passages.text: Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP
negative_passages.docid: 155363
negative_passages.text: Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$