Question

intr-un triunghi dreptunghic ABC,m (<A)=90°,se stie ca AB supra AC =3 supra 4,iar inaltimea AD=24 cm,D apartine (BC). Calculati a)Aria b)Perimetrul repede va roggg

Answer 1

ABC Δ dreptunghic

m(∡A)=90°; AB/AC = 3/4

AB/AC=3/4 ⇒ AB/3=AC/4=k ⇒

AB = 3k si AC = 4k

ΔABC Teorema lui Pitagora⇒

BC²=AB²+AC²=(3k)²+(4k)²=9k²+16k²=25k²

⇒BC=5k

Intr-un triunghi dreptunghic inaltimea este (C₁×C₂)/Ipotenuza

AD = (AB×AC)/BC=(3k×4k)/5k=12k²/5k=12k/5=24 ⇒k=(24×5)/12=10

⇒AB=3k=3×10=30 AC=4k=4×10=40 BC=5k=5×10=50

P = AB+AC+BC=30+40+50 = 120 cm

A = AB×AC/2= 30×40/2 = 600 cm²

Answer 2

Am anexat o rezolvare in plus ----

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