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Question
ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?
Solution
`("A"(Δ"ABP"))/("A"(Δ"DEF")) = 144/81` ......(i)[Given]
`("A"(Δ"ABP"))/("A"(Δ"DEF")) = "AB"^2/"DE"^2` .......(ii)[Theorem of areas of similar triangles]
∴ `"AB"^2/"DE"^2 = 144/81` .......[From (i) and (ii)]
∴ `"AB"/"DE" = 12/9` or `4/3` .......[Taking square root of both sides]
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