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# help

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In the diagram,$$\triangle BDF$$ and $$\triangle ECF$$ have the same area. If $$DB=2,BA=3,$$ find the length of $$\overline{EC}.$$

Feb 12, 2021

#1
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We know that $\triangle BDF$ and $\triangle ECF$ have the same area, and adding the area of quadrilateral $ABFE$ to each of them shows us that$$\text{(area of \triangle ADE)}=\text{(area of \triangle ABC)}.$$Using the area formula for triangles, we can turn the last equation into $$\dfrac{1}{2}\cdot AD\cdot AE = \dfrac{1}{2}\cdot AB\cdot AC.$$Substituting in the given lengths, we get $$\dfrac{1}{2}\cdot 5\cdot 4 = \dfrac{1}{2}\cdot 3\cdot AC,$$so $AC=\dfrac{20}{3}$. We compute the length we are interested in as $EC=AC-AE=\dfrac{20}{3}-4=\boxed{\dfrac{8}{3}}$.

Feb 12, 2021
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Thanks

QuestionMachine  Feb 12, 2021
#3
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no problemo

#4
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Based on the given information, one can argue that these triangles are in fact congruent, and the answer will be a lot different.

btw, where did the number 4 come from? Why not number 3?!?

Guest Feb 12, 2021
edited by Guest  Feb 12, 2021
#5
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You know it's best not to assume.

Feb 12, 2021
#7
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What does tell you that AE = 4?

Guest Feb 12, 2021
#6
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AE is 4 so -AE=-4

Feb 12, 2021
#8
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