if ar(ABC) = 9 and ar(DEF) = 64 and DE = 5.1 find AB
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Answer:
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Step-by-step explanation:
let ∆ABC ~ ∆DEF
We know that the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides
\frac{Ar(ABC)}{Ar(DEF)}
Ar(DEF)
Ar(ABC)
= (\frac{AB}{DE})^2(
DE
AB
)
2
=> \frac{9}{64}
64
9
= (\frac{AB}{DE})^2(
DE
AB
)
2
=> \sqrt{\frac{9}{64}}
64
9
= \frac{AB}{DE}
DE
AB
=> \frac{AB}{5.1}
5.1
AB
= \frac{3}{8}
8
3
=> 8AB = 3 × 5.1
=> AB = 1.9125
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