If TRIANGLE ABC And Triangle DEF are equilateral triangle And A(ABC):A(DEF)=1:2 And if AB =4 THEN DE = ?
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Answer:
Length of the side DE is 4√2.
Step-by-step explanation:
Given: Δ ABC and Δ DEF are Equilateral triangles.
ar(Δ ABC) : ar(Δ DEF) = 1 : 2
AB = 4
To find length of DE.
We know that All Equilateral triangles are similar to each other.
So, we use a result which states that,
If two triangles are similar then ratio of the area of triangles is equal to square to the ratio of the corresponding sides.
So we have,
\frac{\Delta\,ABC}{\Delta\,DEF}=(\frac{AB}{DE})^2
ΔDEF
ΔABC
=(
DE
AB
)
2
\frac{1}{2}=(\frac{4}{DE})^2
2
1
=(
DE
4
)
2
\sqrt{\frac{1}{2}}=\frac{4}{DE}
2
1
=
DE
4
\frac{1}{\sqrt{2}}=\frac{4}{DE}
2
1
=
DE
4
DE=4\sqrt{2}DE=4
2
Therefore, Length of the side DE is 4√2.
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