Răspuns:
Explicație pas cu pas:
2)
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H= punctul de intersectie al medianelor
BB°=27cm
CC°=36 cm
BC=30 cm
CH=2/3*CC°→CH=2/3*36=24
C°H=36-24=12
BH=2/3*BB°→BH=2/3*27 →BH=18
HB°=27-18
HB°=9
↓
CH=24
C°H=12
BH=18
HB°=9
↓
HC°=24
HB==18
BC=30
toate sunt nr pitagorice
↓
aplicam teorema lui Pitagora in Δ HBC
BC²=HC²+HB²
30²=24²+18²
900=900→ΔHBC= triunghi dreptunghic
↓
medianele BB°si CC° sunt ⊥
↓
BB°=AC/2=AC=27*2
BB°=54
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CC°=AB/2=36*2
CC°=72
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AC°=C°B=72/2
AC°=36
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AB°=B°C=54/2
AB°=B°C=54/2=27
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ΔAHC= triunhi dreptunghic
aplicam teorema lui Pitagora
AH²=C°H²+C° A²
AH²=12²+36²
AH²=144+256
AH²=√1440=12√10
AH=2/3*AA°
AA°=(3*12√10)/2→AA°=18√10
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b)
Perimetrul
AB+BC+AC= 54+30+72=156 cm
