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ΔDEF ~ ΔMNK. If DE = 5, MN = 6, then find the value of A(ΔDEF)/A(ΔMNK) - Geometry

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Sum

ΔDEF ~ ΔMNK. If DE = 5, MN = 6, then find the value of `"A(ΔDEF)"/"A(ΔMNK)"`

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Solution

Given: ∆DEF  ∆MNK
by Areas of similar triangles.
`∴ ["A(Δ DEF)"]/["A(Δ MNK)"] = ("DE"^2)/("MN"^2)`

Ratio of areas of Similar Triangles = Ratio of Squares of corresponding sides

`∴ ["A(Δ DEF)"]/["A(Δ MNK)"] = 5^2/6^2 = 25/36`

Concept: Similar Triangles
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