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Question
If ∆ABC ~ ∆PQR and AB : PQ = 3 : 4 then A(∆ABC) : A(∆PQR) = ?
Options
9 : 25
9 : 16
16 : 9
25 : 9
Solution
9: 16
In ∆ABC and ∆PQR,
∆ABC ~ ∆PQR
AB : PQ = 3 : 4 ...(Given)
by theorem of areas of similar triangles,
`"A(∆ABC)"/"A(∆PQR)" = ("AB"^2)/("PQ"^2)`
`"A(∆ABC)"/"A(∆PQR)" = 3^2/4^2`
`"A(∆ABC)"/"A(∆PQR)" = 9/16`.
∴ A(∆ABC) : A(∆PQR) = 9 : 16.
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