Question

Me ajudem ! Teorema de Tales

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Answer 1

4) Os triângulos $AEC$ e $ADB$ são semelhantes pelo caso AAA.

Temos que:

$\dfrac{AD}{AE}=\dfrac{AB}{AC}~~\Rightarrow~~\dfrac{x}{42}=\dfrac{20}{70}$

$\dfrac{x}{42}=\dfrac{2}{7}~~\Rightarrow~~7x=84~~\Rightarrow~~\boxed{x=12~\text{m}}$.

b) $y=AE-AD~~\Rightarrow~~y=42-12~~\Rightarrow~~y=30~\text{m}$.


5) $\dfrac{0,5}{1,60}=\dfarc{1,10}{p}$

$0,5p=1,60\cdot1,10~~\Rightarrow~~0,5p=1,76$

$p=\dfrac{1,76}{0,5}~~\Rightarrow~~p=3,52~\text{m}$.



6) $\dfrac{1}{0,60}=\dfrac{x}{12}$

$0,60x=12~~\Rightarrow~~x=\dfrac{12}{0,6}$

$x=20~\text{m}$.


7) $\dfrac{l}{100}=\dfrac{200}{80}$

$\dfrac{l}{100}=\dfrac{5}{2}$

$2l=500$

$l=250~\text{m}$.