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Omni-MATH / For i=1,2 let T_(i) be a triangle with side lengths a_(i),b_(i),c_(i), and area A_(i). Suppose that a₁≤a₂,b₁≤b₂,c₁≤c₂, and that T₂ is an acute triangle. Does it follow that A₁≤A₂?

Problem

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problem

For i=1,2i = 1,2 let TiT_i be a triangle with side lengths ai,bi,cia_i, b_i, c_i, and area AiA_i. Suppose that a1≤a2,b1≤b2,c1≤c2a_1 \le a_2, b_1 \le b_2, c_1 \le c_2, and that T2T_2 is an acute triangle. Does it follow that A1≤A2A_1 \le A_2?
Plain-text mathematical notation (without MathML)
For i=1,2 let T_(i) be a triangle with side lengths a_(i),b_(i),c_(i), and area A_(i). Suppose that a₁≤a₂,b₁≤b₂,c₁≤c₂, and that T₂ is an acute triangle. Does it follow that A₁≤A₂?
Original LaTeX notation
For $i = 1,2$ let $T_i$ be a triangle with side lengths $a_i, b_i, c_i$, and area $A_i$. Suppose that $a_1 \le a_2, b_1 \le b_2, c_1 \le c_2$, and that $T_2$ is an acute triangle. Does it follow that $A_1 \le A_2$?

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Source and history

task_id
3c6cecd1-f4aa-543a-9eba-7f7fa685c807
task_key
test--3c6cecd1-f4aa-543a-9eba-7f7fa685c807
task_revision_id
1
config / split
/ test

Official source

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