(41C) Area of Triangle (SSS)

11162018, 03:33 AM
(This post was last modified: 12042019 03:05 PM by Albert Chan.)
Post: #12




RE: (41C) Area of Triangle (SSS)
Trivia: Area Δ = √((aby)*y), max(y/(ab)) = 1/4
Prove: gap = ab, y = (c + gap)*(c  gap)/4 dy/dc = 2c > 0, so max(y) when c is also maximize, thus c = b In other words, Δ is isosceles, maybe equilateral (a = b) Let k = a/b, thus 2 > k >= 1: gap = kb  b = b*(k1) y = (b + gap)*(b  gap) / 4 = k*(2k) b² / 4 y/(ab) = y/(kb²) = (2k)/4 > max(y/(ab)) = max(0+ to 1/4) = 1/4 Isosceles Δ, b=c: Area Δ = √((aby)*y) = ab/4 * √((2+k)*(2k)) Equilateral Δ, a=b=c, thus k=1: Area Δ = a²/4 * √3 ~ (√3/4) a² 

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Messages In This Thread 
(41C) Area of Triangle (SSS)  Gamo  11102018, 12:20 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11102018, 03:22 PM
RE: (41C) Area of Triangle (SSS)  Dieter  11102018, 08:53 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11122018, 02:55 PM
RE: (41C) Area of Triangle (SSS)  Dieter  11122018, 08:28 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11122018, 10:33 PM
RE: (41C) Area of Triangle (SSS)  Gamo  11112018, 05:04 AM
RE: (41C) Area of Triangle (SSS)  Dieter  11112018, 07:53 AM
RE: (41C) Area of Triangle (SSS)  Gamo  11112018, 12:23 PM
RE: (41C) Area of Triangle (SSS)  Dieter  11112018, 04:25 PM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11122018, 01:32 AM
RE: (41C) Area of Triangle (SSS)  Albert Chan  11162018 03:33 AM
RE: (41C) Area of Triangle (SSS)  Albert Chan  12042019, 03:03 PM

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