Răspuns:
Explicație pas cu pas:
b
BD=18 cm ;BC=50 cm
CD=BC-BD=50-18=32 cm
T Catetei AC²=CD·BC=32·50 ⇒AC=√32·50=√2^5·2·5²
AC=2³·5=40 cm
AB²=BD·BC=18·50 ⇒AB=√2·3²·2·5²=2·3·5=30 cm
T Inaltimii AD²=BD·BC=18·32 ⇒AD=√2·3²·2^5=2³·3=24 cm
c
CD=6 cm ; AC=6√3 cm
AC²=CD·BC ⇒36·3=6·BC ⇒BC=18 cm
BD=BC-CD ⇒BD=18·6=12 cm
AB²=BD·BC ⇒AB²=12·18 ⇒AB=√2²·3·3²·2=6√6 cm
AD=AB·AC/BC=6√6/18=√6/3 cm
d
BC=4 cm ; AC=√11 cm
T Pitagora
AB²+AC²=BC² ⇒AB²=BC²-AC²=16-11=5 ⇒AB=√5 cm
T Catetei BD=AB²/BC si CD=AC²/BC
BD=5/4=1.25cm CD=11/4=2,75 cm
AD=AB·AC/BC=√5·√11/4=√55/4 cm
e
BD=7 cm AD=3√14 cm
T Inaltimii AD²=BD·CD ⇒9·14=7·CD ⇒CD=9·2=18 cm
BC=BD+CD=7+18 =25 cm
T catetei AB²=BD·BC AB²=7·25 ⇒AB=5√7 cm
AC²=CD·BC ⇒AC²=18 ·25 ⇒AC=√2·3²·5²=3·5√2=15√2 cm
