Răspuns:
Explicație pas cu pas:
1) AB²=BD*BC
BC=AB²/BD = 4²/2=16/2=8cm
AB²+AC²=BC²
AC=√(BC²-AB²)=√(8²-4²)=√(64-16)=√(48)=4√3cm
AB=4cm, AC=4√3cm, BC=8cm
2) AC²=CD*BC
BC=AC²/CD = 6²/4=36/4=9cm
AB²+AC²=BC²
AB=√(BC²-AC²)=√(9²-6²)=√(81-36)=√(45)=3√5cm
AB=3√5cm, AC=6cm, BC=9cm
3) BC=CD+BD=4+5=9cm
AC²=CD*BC
AC=√(CD*BC)=√(4*9)=√36=6cm
AB²=BD*BC
AB=√(BD*BC)=√(5*9)=√45=3√5cm
AB=3√5cm, AC=6cm, BC=9cm
4) AB²=AD²+BD²
AB=√(AD²+BD²)=√[(3√5)² + 5²]=√(45 + 25)=√80=4√5cm
AB²=BD*BC
BC=AB²/BD = (4√5)²/5=80/5=16cm
BC²=AB²+AC²
AC=√(BC²-AB²)=√[16² - (4√5)²]=√(256-80)=√176=4√11cm
AB=4√5cm, AC=4√11cm, BC=16cm
5) AB²+AC²=BC²
AB=√(BC²-AC²)=√(13²-5²)=√(169-25)=√(144)=12cm
AB=12cm, AC=5cm, BC=13cm
6) AB²+AC²=BC²
AB=√(BC²-AC²)=√[6²-(4√2)²]=√(36-32)=√(4)=2cm
AB=2cm, AC=4√2cm, BC=6cm
7) AB²=AD²+BD²
BD=√(AB²-AD²)=√(3² - 2,4²]=√(9 -- 5,76)=√3,24=1,8m
AB²=BD*BC
BC=AB²/BD = 3²/1,8=9/1,8=5m
BC²=AB²+AC²
AC=√(BC²-AB²)=√(5² - 3²]=√(25-9)=√16=4m
AB=3m, AC=4m, BC=5m
8) AC²=CD*BC
AC=√(CD*BC) =√(5,4*15) =√81 =9m
AB²+AC²=BC²
AB=√(BC²-AC²)=√(15²-9²)=√(225-81)=√(144)=12m
AB=12m, AC=9m, BC=15m
9) AC²=AD²+DC²
AC=√(AD²+DC²)=√[(3√3)² + 9²]=√(27 + 81)=√108=6√3m
AC²=DC*BC
BC=AC²/DC = (6√3)²/9=108/9=12m
BC²=AB²+AC²
AB=√(BC²-AC²)=√[12² - (6√3)²]=√(144-108)=√36=6m
AB=6m, AC=6√3m, BC=12m
