Răspuns: [tex]\bf Aria_{\Delta ABC} =160~m^{2}[/tex]
Explicație pas cu pas:
Salutare!
[tex]\bf D \in [AB]\implies [AD]=[DB][/tex]
[tex]\bf E \in [BC]\implies [BE]=[EC][/tex]
[tex]\bf Aria_{\Delta DBE} = \dfrac{[DB]\cdot[BE]}{2}[/tex]
[tex]\bf 40~m^{2}= \dfrac{[DB]\cdot[BE]}{2} \implies[DB]\cdot[BE] = 2\cdot 40\implies \boxed{ \bf [DB]\cdot[BE] = 80}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{[AB]\cdot[BC]}{2}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{([AD]+[DB])\cdot([BE]+[EC])}{2}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{([DB]+[DB])\cdot([BE]+[BE])}{2}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{2[DB]\cdot 2[BE]}{2}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{4\cdot [DB]\cdot [BE]}{2}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{\not4\cdot 80}{\not2}[/tex]
[tex]\bf Aria_{\Delta ABC} = \dfrac{2\cdot 80}{1}[/tex]
[tex]\boxed{\boxed{\bf Aria_{\Delta ABC} =160~m^{2}}}[/tex]
Varianta: c) 160 m²
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