Explicație pas cu pas:
ΔMDC ~ ΔMAB
[tex]\frac{MD}{MA} = \frac{DC}{AB} = \frac{MC}{MB} \iff \\ \frac{MD}{MA - MD} = \frac{DC}{AB - DC} = \frac{MC}{MB - MC} \\ [/tex]
[tex]\frac{MD}{AD} = \frac{DC}{AB - DC} = \frac{MC}{BC} \iff \\ \frac{MD}{9} = \frac{10}{25 - 10} = \frac{MC}{12} \\ [/tex]
[tex]\frac{MD}{9} = \frac{MC}{12} = \frac{2}{3} \\ MD = \frac{9 \times 2}{3} \implies MD = 6 \: cm \\ MC = \frac{12 \times 2}{3} \implies MC = 8 \: cm[/tex]
a) perimetrul ΔMDC = MD + MC + CD = 6 + 8 + 10 = 24 cm
b)
[tex]\frac{DC}{AB} = \frac{10}{25} = \frac{2}{5} \\ [/tex]
[tex]\frac{Aria_{\triangle MDC}}{Aria_{\triangle MAB}} = {\left( \frac{2}{5}\right)}^{2} = \frac{4}{25} = \frac{16}{100} \\ [/tex]
[tex]\implies Aria_{\triangle MDC} = 16\% \cdot Aria_{\triangle MAB} \\ [/tex]
=> p = 16
