Question

Intr-un triunghi dreptunghic raportul lungimilor catetelor este egal cu 3/4 iar lungimea ipotenuzei este egala cu 40 cm. Calculati: lungimea catetelor
triunghiului dat si perimetrul triunghiulei.

Answer 1

$\Delta ABC-tr. \ dreptunghic \\\\ \frac{c_1}{c_2}= \frac{3}{4} \\\\\\ \frac{c_1}{3}=\frac{c_2}{4}=k \ \ ; k \in N\\\\ c_1=3k \\ c_2=4k \\\\\\ c_1^2+c_2^2=i^2 \\\\ (3k)^2+(4k)^2=40^2 \\\\ 9k^2+16k^2=1600 \\\\ 25k^2=1600 \ \ |:25 \\\\ k^2=64 \\\\ \boxed{k=8} \\\\ c_1=3*8 \\\\ \boxed{\boxed{c_1=24}} \\\\ c_2=4*8 \\\\ \boxed{\boxed{c_2=32}} \\\\\\ P_{\Delta}=c_1+c_2+i = 24+32+40 \longrightarrow 96$

Answer 2

C1 si C2-catete
ip-ipotenuza


C1/C2=3/4 => C1=3C2 supra 4
C1la2 +  C2la2 = ip la a 2

9 C2la2/16 +  C la2 =1600
9 C2la2/16 + 16C2la2/16= 25600/16
C2la2=25600/25
C2 la2= 1024
C2= √1024
C2=32 cm

C1=3C2/4=
C1=3x32/4
C1=24 cm

Perimetrul=C1+C2+Ip=32+24+40=96 cm