Question

In the given figure, PM = 10 cm A(∆PQS) = 100 sq.cm A(∆QRS) = 110 sq.cm then Find NR.

Answer 1

Given:
PM = 10 cm
A(∆PQS) = 100 sq.cm
A(∆QRS) = 110 sq.cm
$$\begin{gathered} \mathrm{Now},\frac{\mathrm{A}\left(∆\mathrm{PQS}\right)}{\mathrm{A}\left(∆\mathrm{QRS}\right)}=\frac{100}{110} \\ \Rightarrow \frac{{\displaystyle \frac{1}{2}\times \mathrm{PM}\times \mathrm{QS}}}{{\displaystyle \frac{1}{2}\times \mathrm{RN}\times \mathrm{QS}}}=\frac{10}{11} \end{gathered}$$​
​$$\begin{gathered} \Rightarrow \frac{{\displaystyle 10}}{{\displaystyle \mathrm{RN}}}=\frac{10}{11} \\ \Rightarrow \mathrm{RN}=11\mathrm{cm} \end{gathered}$$