Question

Ajutor, please very muci ​

Answer 1

Răspuns:  216 cm²

Explicație pas cu pas:

AB/AC = 3/4

AB = 3k

AC = 4k

BC² = AB² + AC²

BC² = (3k)² + (4k)²

30² = 9k² + 16k²

900 = 25k²

k² = 900 : 25

k² = 36

k = √36

k = 6

AB = 3 x 6 = 18 cm

AC = 4 x 6 = 24 cm

Aria = cateta1 x cateta2 / 2

A = AB x AC / 2 = 18 x 24/2 = 9 x 24 = 216 cm²

Answer 2

Explicație pas cu pas:

ABC triunghi dreptunghic, ∢A = 90°, BC = 30 cm

$\frac{AB}{AC} = \frac{3}{4} = >AB = \frac{3AC}{4}$

AB² + AC² = BC²

$(\frac{3AC}{4})^{2} + AC^{2} = BC^{2} \\ \frac{9AC^{2} }{16} + AC^{2} = 900 = > \frac{25AC^{2} }{16} = 900 \\ AC^{2} = \frac{16 \times 900}{25} = 576 = > AC = 24 \: cm \\ AB = \frac{3 \times 24}{4} = > AB = 18 \: cm$

=>

$Aria_{ABC} = \frac{AB \times AC}{2} = \frac{18 \times 24}{2} = 216 \: {cm}^{2}$