Question

in triunghiul ABC, unghiul A=90°,AD perpendicular pe BC,D apartine BC,AC=40cm,CD=32cm. Se cere BC,BD,AB,AD​

Answer 1

Răspuns:

Explicație pas cu pas:

Teorema catetei

AC²=CD·BC    ⇒1600=32·BC   ⇒BC=1600/32=50 cm

BD=BC-CD=50-32=18 cm

AB²=BD·BC    ⇒AB²=18·50=2²·3²·5²   ⇒AB=30 cm

Teorema Inaltimii

AD²=BD·CD=18·32=2·3²·2^5=2^6·3²   ⇒AD=2³·3=24 cm

Answer 2

Răspuns:

BC=50 cm

BD=18 cm

AB=30 cm

AD=24 cm

Explicație pas cu pas:

AC=40 cm   CD=32 cm

AD=√(AC²-CD²)=√(40²-32²)=√(1600-1024)=√576=24 cm   AD=24 cm

AD²=CD·BD  ⇒BD=AD²:CD=24²:32=576:32=18 cm BD=18 cm

BC=BD+DC=18+32=50 cm   BC=50 cm

AB=√(BC²-AC²)=√(50²-40²)=√(2500-1600)=√900=30 cm  AB=30 cm.