Question

4. Dacă AABC~ AMNP, AB = 8 cm, BC = 12 cm, AC = 16 cm, MN= 6 cm, calculați perimetrul triunghiului MNP.​

Answer 1

Explicație pas cu pas:

ΔABC ~ ΔMNP, AB = 8 cm, BC = 12 cm, AC = 16 cm, MN= 6 cm

$\dfrac{AB}{MN} = \dfrac{BC}{NP} = \dfrac{AC}{MP} = \dfrac{AB + BC + AC}{MN + NP + MP} = \\ = \dfrac{8 + 12 + 16}{\mathcal{P}_{\triangle MNP}} = \dfrac{36}{\mathcal{P}_{\triangle MNP}}$

$\dfrac{36} {\mathcal{P}_{\triangle MNP}} = \dfrac{AB}{MN} \iff \dfrac{36} {\mathcal{P}_{\triangle MNP}} = \dfrac{8}{6} \\ \implies \mathcal{P}_{\triangle MNP} = 27 \ cm$