Explicație pas cu pas:
ABC triunghi dreptunghic, ∢A = 90°, BC = 30 cm
[tex]\frac{AB}{AC} = \frac{3}{4} = >AB = \frac{3AC}{4} \\ [/tex]
AB² + AC² = BC²
[tex](\frac{3AC}{4})^{2} + AC^{2} = BC^{2} \\ \frac{9AC^{2} }{16} + AC^{2} = 900 = > \frac{25AC^{2} }{16} = 900 \\ AC^{2} = \frac{16 \times 900}{25} = 576 = > AC = 24 \: cm \\ AB = \frac{3 \times 24}{4} = > AB = 18 \: cm \\ [/tex]
=>
[tex]Aria_{ABC} = \frac{AB \times AC}{2} = \frac{18 \times 24}{2} = 216 \: {cm}^{2} \\ [/tex]
