Răspuns:
Explicație pas cu pas:
★Perimetrul unui triunghi inseamna suma lungimilor laturilor triunghiului
Pabc=AB+AC+BC
Pabc=72 cm => AB +AC+BC=72
[tex]\displaystyle \frac{AB}{AC} =\frac{3}{4} => AB=\frac{3}{4} \times AC[/tex]
Δ ABC dreptunghic => teorema lui Pitagora =>
[tex]\displaystyle BC^{2} =AB^{2} +AC^{2} \\BC^{2} =(\frac{3}{4} \times AC)^2 +AC ^{2} \\ BC^{2} =\frac{9}{16} \times AC^{2} + AC^{2}\\BC^{2} =\frac{9AC^{2}+16AC^{2} }{16} \\ BC^{2} =\frac{25AC^{2} }{16} \\BC=\sqrt{\frac{25AC^{2} }{16} } \\ BC=\frac{5}{4} \times AC[/tex]
[tex]\displaystyle AB+AC+BC=72\\\\ \frac{3}{4}\times AC +AC + \frac{5}{4} \times AC=72\\\\ \frac{8}{4} \times AC+AC=72\\ \\ 2AC+AC=72\\\\ 3AC=72\\\\ AC=72:3\\\\ AC=24[/tex]
[tex]\displaystyle AB= \frac{3}{4} \times AC =\frac{3}{\not4} \times \not24= 3\times 6=18\\ \\ BC = \frac{5}{4} \times AC=\frac{5}{\not4}\times\not 24 = 5\times 6=30[/tex]
Aria unui triunghi drept este produsul catetelor impartit la 2
[tex]\displaystyle A=\frac{AB\times AC}{2} =\frac{\not24 \times 18}{\not2} = 12\times 18=216 cm^{2}[/tex]
