Question

(Sp) 4. In figura alaturata, triunghiul ABC reprezinta
o gradina. Zona haşurată are aria egală cu 40 m²
Punctele D si E sunt mijloacele segmentelor AB,
respectiv BC. Aria triunghiului ABC este egală cu:
a) 80 m2
b) 120 m2
c) 160 m2
d) 200 m2
B

Answer 1

Răspuns: $\bf Aria_{\Delta ABC} =160~m^{2}$

Explicație pas cu pas:

Salutare!

$\bf D \in [AB]\implies [AD]=[DB]$

$\bf E \in [BC]\implies [BE]=[EC]$

$\bf Aria_{\Delta DBE} = \dfrac{[DB]\cdot[BE]}{2}$

$\bf 40~m^{2}= \dfrac{[DB]\cdot[BE]}{2} \implies[DB]\cdot[BE] = 2\cdot 40\implies \boxed{ \bf [DB]\cdot[BE] = 80}$

$\bf Aria_{\Delta ABC} = \dfrac{[AB]\cdot[BC]}{2}$

$\bf Aria_{\Delta ABC} = \dfrac{([AD]+[DB])\cdot([BE]+[EC])}{2}$

$\bf Aria_{\Delta ABC} = \dfrac{([DB]+[DB])\cdot([BE]+[BE])}{2}$

$\bf Aria_{\Delta ABC} = \dfrac{2[DB]\cdot 2[BE]}{2}$

$\bf Aria_{\Delta ABC} = \dfrac{4\cdot [DB]\cdot [BE]}{2}$

$\bf Aria_{\Delta ABC} = \dfrac{\not4\cdot 80}{\not2}$

$\bf Aria_{\Delta ABC} = \dfrac{2\cdot 80}{1}$

$\boxed{\boxed{\bf Aria_{\Delta ABC} =160~m^{2}}}$

Varianta: c) 160 m²

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