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Question
∆LMN ~ ∆PQR, 9 × A (∆PQR ) = 16 × A (∆LMN). If QR = 20 then Find MN.
Solution
Given:
QR = 20
∆LMN ~ ∆PQR
9 × A (∆PQR ) = 16 × A (∆LMN)
Consider, 9 × A (∆PQR ) = 16 × A (∆LMN)
\[\frac{A\left( ∆ LMN \right)}{A\left( ∆ PQR \right)} = \frac{9}{16}\]
\[ \Rightarrow \frac{{MN}^2}{{QR}^2} = \frac{3^2}{4^2}\]
\[ \Rightarrow \frac{MN}{QR} = \frac{3}{4}\]
\[\Rightarrow MN = \frac{3}{4} \times QR\]
\[ \Rightarrow MN = \frac{3}{4} \times 20 \left[ \because QR = 20 \right]\]
\[ \Rightarrow MN = 15\]
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