Explicație pas cu pas:
M este mijlocul catetei AC => AM ≡ MC = 10 cm
T.P.: AC² = BC² - AB² = 25² - 20² = 225 = 15²
=> AC = 15 cm
ΔBAC ~ ΔMNC
[tex]\frac{AB}{MN} = \frac{AC}{NC} = \frac{BC}{MC} \\ \implies \frac{15}{MN} = \frac{20}{NC} = \frac{25}{10} = \frac{5}{2} [/tex]
[tex]MN = \frac{2 \cdot 15}{5} \implies MN = 6 \: cm \\ NC = \frac{2 \cdot 20}{5} \implies NC = 8 \: cm[/tex]
BN = BC - NC = 25 - 8 => BN = 17 cm
[tex]P_{ABNM} = AB + BN + NM + AM = \\ = 15 + 17 + 6 + 10 = \red{\bf 48 \: cm}[/tex]
