Fie triunghiul isoscel ABC cu AB=AC=25cm si Inaltimea corespunzatoare bazei de 20 cm. Aflati aria triunghiului ABC.
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Răspuns:
Explicație pas cu pas:
fie AD inaltimea din A
AD=mediana,ABC fiind isoscel AB=AC
conform Pitagora
BD= rad din (625-400)=15 cm
BC=2*BD=30
aria =20*30/2=300 cm 2
[tex]\it \mathcal{A}=\sqrt{p(p-a)(p-b)(p-c)}\\ \\ p=\dfrac{a+b+c}{2}=\dfrac{20+25+25}{2}=\dfrac{70}{2}=35\\ \\ \\ p-a=35-20=15\\ \\ p-b=p-c=35-25=10\\ \\ \\ \mathcal{A}=\sqrt{35\cdot15\cdot10\cdot10}=\sqrt{7\cdot5\cdot5\cdot3\cdot100}=\sqrt{100\cdot25\cdot21}=50\sqrt{21}\ cm^2[/tex]