Question

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

Answer 1

$\mathfrak{ANSWER:-}\\MN = 15\:UNITS\:\\\\\mathfrak{STEP\: BY \:STEP\: EXPLAINATION:-}\\GIVEN -\\\Delta LMN \sim \Delta PQR\\Consider, \: 9 \times A(\Delta PQR) = 16\times A(\Delta LMN)\\\frac{A(\Delta LMN)}{A(\Delta PQR)} = \frac{9}{16}\\\therefore \: BY\:USING\:Theorem \: of \: areas \: of \: similar\: triangles\\\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$$\\\Rightarrow MN = 15\\\mathbf{HOPE\:IT\:MAY\:HELP\:YOU}$