Question

Va roggg Am nevoie de aceste exercitii. Doar 5 si 6 MA abonezzz dau 100 de pcte! Chiar am nevoie de ele... ​

Answer 1

5.

$A=\frac{MP\times NQ}{2} \\\\8\sqrt{6}\times 2= 4\sqrt{6} \times NQ\\\\NQ=4\ cm$

Fie {O}=MP∩NQ

MO=2√6

NO=2

Aplicam Pitagora in ΔMON dr in O

MN²=24+4=28

MN=2√7 cm

$P_{MNPQ}=4MN=8\sqrt{7} \ cm$

6.

L=15 cm

l=10 cm

Aplicam Pitagora in ΔBD dr in A

BD²=AD²+AB²

BD²=225+100=325

BD=5√13 cm

P=AB+BD+AD=25+5√13

5√13≅18

25+18=43<45

Fie EF⊥CD, EF║BC

AE bis ⇒ Teorema bisectoarei

$\frac{AD}{AB} =\frac{DE}{EB} \\\\\frac{DE}{EB}=\frac{10}{15}=\frac{2}{3}$

$\frac{DE}{DE+EB}= \frac{2}{2+3} \\\\\frac{DE}{DB} =\frac{2}{5}$

EF║BC⇒

$\frac{DE}{DB} =\frac{DF}{DC} =\frac{EF}{BC} \\\\\frac{DE}{DB} =\frac{EF}{BC}\\\\\frac{2}{5} =\frac{EF}{10}$

EF=4 cm

$\frac{2}{5} =\frac{DF}{15}$

DF=6 cm⇒FC=9 cm

Aplicam Pitagora in EFC dr in F

EC²=EF²+FC²

EC²=16+81

EF=√97cm