Question

determine o perímetro do triângulo CDE na figura a seguir.​

Answer 1

Resposta:

$72$

Explicação passo-a-passo:

$DC^2 = 12^2 + 16^2\\DC^2 = 144 + 256\\DC^2 = 400\\DC = 20$

$\dfrac{EC}{AB} = \dfrac{DC}{x + EC}$

$\dfrac{16}{24} = \dfrac{20}{x + 16}$

$480 = 16x + 256$

$16x = 224$

$x = 14$

$\dfrac{EC}{AB} = \dfrac{DE}{x + DE}$

$\dfrac{16}{24} = \dfrac{12}{x + 12}$

$288 = 16x + 192$

$16x = 96$

$x = 6$

$AB = 24\\BC = 14 + 16 = 30\\AC = 6 + 12 = 18$

$\boxed{\boxed{P = AB + BC + AC = 24 + 30 + 18 = 72}}$