Question

Ajutooor cat de repede posibill !!dau coroana si puncteeeee
ABC triunghi dreptunghic in B
BD_|_ AC şi D€ [ AC ] sa se afle : a ) perimetrul triunghiului ABC daca se cunosc AD=4 cm şi DC = 5 cm.
b )AB şi BC daca se stie AC=30 cm si raportul dintre AD şi DC este 1 /4 .

Fara desen , doar rezolvarea ptr fiecare subpunct !!

Answer 1

a)
AC=AD+DC⇔
⇔AC=4+5⇔
⇔AC=9

ΔABC dreptunghic )⇒cat²=pr·ip⇔
m(∡ABC)=90°        )⇔AB²=AD·AC⇔
                                ⇔AB²=4·9⇔
                                ⇔AB²=36|·√⇔
                                ⇔√AB²=6 cm

ΔABC dreptunghic)⇒ ip²=cat²+cat²⇔
m(∡ABC)=90°       )   ⇔AC²=AB²+BC2⇔
                                  ⇔9²=6²+BC²⇔
                                  ⇔36+BC²=81⇔
                                  ⇔BC²=81-36⇔
                                  ⇔BC²=45|·√⇔
                                  ⇔√BC²=√45⇔
                                  ⇔BC=3√5

PΔABC=AB+AC+BC⇔
⇔PΔABC=6+9+3√5⇔
⇔PΔABC=15+3√5⇔
⇔PΔABC=5·3+3·√5⇔
⇔PΔABC=3(5+√5)


b)
AB/DC=1/4⇔
⇔AD+DC/DC=1+4/4⇔
⇔AC/DC=5/4⇔
⇔30/DC=5/4⇔
⇔DC=30·4/5⇔
⇔DC=34 cm

AC=AD+DC⇔
⇔AD+DC=AC⇔
⇔AD+24=30⇔
⇔AD=30-24⇔
⇔AD=6 cm

SPER CA TE-AM AJUTAT^^