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DeltaLMN~DeltaPQR, 9xxA(DeltaPQR)=16xxA(...

`DeltaLMN~DeltaPQR`, `9xxA(DeltaPQR)=16xxA(DeltaLMN)`. If `QR=20`, then find `MN`.

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`DeltaLMN~DeltaPQR`……(Given)
`9xxA(DeltaPQQR)=16xxA(DeltaLMN)`
`:.(A(DeltaLMN))/(A(DeltaPQR))=(9)/(16)` ……..`(1)`
Now, `(A(DeltaLMN))/(A(DeltaPQR))=(MN^(2))/(QR^(2))`……. (Theorem of areas of similar triangle)…………`(2)`
`:.(9)//(16)=(MN^(2))/(QR^(2))`......[From `(1)` and `(2)`]
`:.(MN)/(QR)=(3)/(4)`......[Taking square roots on both the sides)
`:.(MN)/(20)=(3)/(4)`........(`QR=20`, given)
`:.MN=(20xx3)/(4) :.MN =15`
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