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

Explanation

`DletaLMN~DletaPQR` ……….(Given)
`9xxA(DeltaPQR)=16xxA(DeltaLMN)`
`:.(A(DeltaLMN))/(A(DeltaPQR))=9/16`…………..1
Now `(A(DeltaLMN))/(A(DeltaPQR))=(MN^(2))/(QR^(2))`
`:.9/16=(MN^(2))/(QR^(2))` ………..[From 1]
`:.(MN)/(QR)=3/4`
……….(Taking square roots on both the sides)
`:.(MN)/20=3/4` ...........( `:'QR=20` given)
`:.MN=(20xx3)/4:.MN=15`
`MN=15`.