Question

ajutati maaaa de terminat acest exercitiu​

Answer 1

Explicație pas cu pas:

b)

MN || AB => ΔABC ~ ΔNMC

$\dfrac{AB}{MN} = \dfrac{AC}{NC} = \dfrac{BC}{MC} = k$

k = raport de asemănare

Raportul ariilor a două triunghiuri asemenea este egal cu pătratul raportului de asemănare.

$\dfrac{\mathcal{A}_{\Delta ABC}}{\mathcal{A}_{\Delta NMC}} = \bigg(\dfrac{AB}{MN}\bigg)^{2} \iff \dfrac{\mathcal{A}_{\Delta ABC}}{\mathcal{A}_{\Delta NMC}} = k^{2}$

$\dfrac{\mathcal{A}_{\Delta ABC}}{\mathcal{A}_{\Delta NMC}} = \dfrac{25}{4} = \bigg(\dfrac{5}{2}\bigg)^{2} \iff k = \dfrac{5}{2}$

$\dfrac{AB}{MN} = \dfrac{5}{2} \iff \dfrac{10}{MN} = \dfrac{5}{2} \\ \\ \implies MN = 4 \ cm$