Question

1.Daca ∆ABC~∆MNP,AB/MN=2/5 și P[ABC]=12 cm,determinați P[MNP]
2.Dacă ∆ABC~∆MNP,AB/MN=1/2 și A[ABC]=8 cm^2, determinați A[MNP]

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

1.

$\it \Delta ABC\sim \Delta MNP;\ \ \dfrac{AB}{MN}=\dfrac{2}{5}=k\ \ (raportul\ de\ asem\breve a nare)\\ \\ \dfrac{\mathcal{P}_{ABC}}{\mathcal{P}_{MNP}}=k \Rightarrow \dfrac{12}{\mathcal{P}_{MNP}}=\dfrac{^{6)}2}{\ \ 5} \Rightarrow \dfrac{12}{\mathcal{P}_{MNP}}=\dfrac{12}{30} \Rightarrow\mathcal{P}_{MNP}=30\ cm$

2.

$\it \Delta ABC\sim \Delta MNP;\ \ \dfrac{AB}{MN}=\dfrac{1}{2}=k\ \ (raportul\ de\ asem\breve a nare)\\ \\ \dfrac{\mathcal{A}_{ABC}}{\mathcal{A}_{MNP}}=k ^2\Rightarrow \dfrac{8}{\mathcal{A}_{MNP}}=\dfrac{^{8)}1}{\ \ 4} \Rightarrow \dfrac{8}{\mathcal{A}_{MNP}}=\dfrac{8}{32} \Rightarrow\mathcal{A}_{MNP}=32\ cm^2$