Răspuns:
Explicație pas cu pas:
Intr-un triunghi dreptunghic ABC , unghiul A =90 grade , AD perpendicular BC, D apartine (BC) , se dau :
a) AB =16 cm si BC =20cm.Se cer BD,DC,AC,AD si Aria ABC
T. Pitagora AC=√(BC²-AB²)=√(20²-16²)=√(400-256)=√144=12 AC=12 cm.
T. catetei: AC²=BC·CD ⇒144=20·CD ⇒CD=144:20 ⇒CD=7,2 cm.
AB²=BC·BD ⇒256=20·BD ⇒BD=256:20 ⇒BD=12,8 cm.
T. inaltimii: AD²=CD·BD=7,2·12,8=92,16 ⇒AD=√92,16=9,6 cm.
Aria ABC =cateta1·cateta2/2=12·16/2=6·16=96 cm² Aria=96 cm²
b) BC =50cm su BD =32cm.Se cer DC,AD,AB,AC si Aria ABC
DC=BC-BD=50-32=18 cm. DC=18 cm.
T. inaltimii: AD²=CD·BD=18·32=576 ⇒AD=√576=24 cm. AD=24 cm.
AB²=AD²+BD²=24²+32²=576+1024=1600 ⇒AB=√1600=40 AB=40 cm.
AC²=BC²-AB²=50²-40²=2500-1600=900 ⇒AC=√900=30 AC=30 cm.
Aria ABC =cateta1·cateta2/2=30·40/2=600 cm² Aria ABC=600 cm²
c) AC =20cm si DC =16cm.Se cer BD,BC,AB,AD si Aria ABC
AD²=AC²-CD²=20²-16²=400-256=144 ⇒AD=√144=12 AD=12 cm.
T. inaltimii: AD²=CD·BD=16·BD ⇒BD=12²/16=144/16=9 BD=9 cm.
BC=BD+DC=9+16=25 BC=25 cm.
T. Pitagora AB=√(BC²-AC²)=√(25²-20²)=√(625-400)=√225=15 ⇒
AB=15 cm.
Aria ABC =cateta1·cateta2/2=20·15/2=150 cm² Aria ABC = 150 cm²
