α
2
b hA
perímetro
per a b c
1 2
2
cat catA
( )( )( )
2
Fórmula de Herão
A m m a m b m c
perímetroonde m
perímetro
per a b c
1 2
perímetro
per cat cat hip
per b c a
2 3
4A
3per
3
3
15(15− 5)(15− 12)(15− 13)
15(10)(3)(2)
900
2
2
dA
∆ABC ~ ∆ACH
𝑎
𝑏=𝑏
𝑚
𝑏
2= 𝑎.𝑚
∆ABC ~ ∆ABH
a
c=
c
n
𝑐2 = 𝑎.𝑛
∆ABH ~ ∆ACH
𝑏
𝑐=𝑚
ℎ=ℎ
𝑛
ℎ2 = 𝑚.𝑛
∆ABC ~ ∆ACH
a
b=
c
h
𝑎.ℎ = 𝑏. 𝑐
𝑚 + 𝑛 = 𝑎
𝑚 =𝑏2
𝑎 𝑛 =
𝑐2
𝑎
𝑏2
𝑎+𝑐2
𝑎= 𝑎
𝑏2 + 𝑐2
𝑎= 𝑎
𝑏2 + 𝑐2 = 𝑎2
𝒂𝟐 = 𝒃𝟐 + 𝒄𝟐
a = m. n
a = 18 + 32
𝑎 = 50
𝑏² = 𝑎.𝑚
𝑏² = 50.18
𝑏² = 900
𝑏 = 30
𝑐² = 𝑎.𝑛
𝑐² = 50.32
𝑐² = 1600
𝑐 = 40
𝑎.ℎ = 𝑏. 𝑐
50.ℎ = 30.40
ℎ =30.40
50
ℎ = 24
𝑐2 = 𝑎.𝑛
𝑐2 = 16.12
𝑐2 = 192
𝑐 = 192
𝑐 = 26 . 3
𝑐 = 22 . 22 . 22 . 3
𝑐 = 8 3
ℎ2 = 𝑚.𝑛
ℎ2 = 4.12
ℎ2 = 48
ℎ = 48
ℎ = 2222. 3
ℎ = 4 3
𝐵𝐻 = 𝑚
𝑚 = 16− 12
𝑚 = 4
h2 = m. n
h2 = 9.4
h2 = 36 h = 6
𝑎.ℎ = 𝑏. 𝑐
25.ℎ = 15.20
ℎ =15.20
25
ℎ = 12
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