Question

∆LMN ~ ∆PQR, 9 × A (∆PQR ) = 16 × A (∆LMN). If QR = 20 then Find MN. 

Answer 1

Given:

QR = 20

∆LMN ~ ∆PQR

9 × A (∆PQR ) = 16 × A (∆LMN)

Consider, 9 × A (∆PQR ) = 16 × A (∆LMN) 

\[\frac{A\left( ∆ LMN \right)}{A\left( ∆ PQR \right)} = \frac{9}{16}\]

\[ \Rightarrow \frac{{MN}^2}{{QR}^2} = \frac{3^2}{4^2}\]

\[ \Rightarrow \frac{MN}{QR} = \frac{3}{4}\] 

\[\Rightarrow MN = \frac{3}{4} \times QR\]

\[ \Rightarrow MN = \frac{3}{4} \times 20 \left[ \because QR = 20 \right]\]

\[ \Rightarrow MN = 15\]