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Nechitamagdale
a fost răspuns

Fie Δ dreptunghic ABC cu m(
c) Daca CD=√15 cm si AC 3√10 cm,calculati BC si AB.
d) Daca AB=24 cm si BC=48 cm,calculati BD si AC.

Răspuns :

StanciuGabriela29
ΔABC, AC=3√10, CD= √15
AD _|_ BC

ΔADC (unghiul D=90)
AD²= AC²-CD² = 90-15 = 75 => AD=5√3
Folosim o formula pt inaltime:
AD²= BD*DC => 75 = BD* √15 => BD = 75/√15
BC = BD+DC = 75/√15+ √15 = 90/√15

AD = (AB*AC)/BC => 5√3= (AB*3√10)/ (90/√15)
90*5√3 = AB * 3√10 *√15 = > AB = 450√3 / 5√6

ΔABC, AB = 24 , BC = 48
BC²= AB²+AC² => AC = 24√3

AD = (AB*AC)/BC = (24*24√3)/48 = 12√3

Mariusel01
a)ΔABC cf teoremei catetei: AC²=CD·CB; 90=√15·CB⇒CB=90/√15=6√15
in acelasi Δ cf pitagora: AB²=CB²-AC²=540-90=450
AB=15√2
B)ΔABC cf teoremei catetei:AB²=BD·DC
24²=BD·48
BD=12
CD=48-12=36
acelasi tr cf teoremei catetei: AC²=CD·DB=36·12
AC=12√3
Vezi imaginea Mariusel01