Question

Triangle LMN~trianglePQR 9xA(trianglePQR)=16xA(triangleLMN) if QR=20 then find MN

Answer 1

$\mathtt{\huge{ \fbox{Solution}}}$

Given that ∆LMN and ∆PQR similar triangles.

9 × Area of ∆PQR = 16 × Area of ∆LMN

$\sf {Area \of\ \Delta LMN : Area\ of\ \Delta PQR = 9:16}$

∵ Area of two similar triangles is = Square of their corresponding sides.

Thus,

$\sf {\frac{Area\ of\ \Delta LMN}{Area \ of \ \Delta PQR } =(\frac{MN}{QR})^{2} }\\\\\\\sf {\Rightarrow \frac{9}{16}=\frac{MN^{2}}{20^{2}}}\\\\\\\sf {\Rightarrow MN^{2}=\frac{9 \times 20^{2}}{16}}\\\\\\\sf {\Rightarrow MN =\sqrt{\frac{9 \times 400}{16} } }\\\\\\\sf {\Rightarrow \frac{3 \times 20}{4} }$

⇒ 3 × 5 = 15 cm