Question

(a) In the given figure, LM|| QR Find PL.



(b) In $\Delta ABC,DE||BC.IfAD=x-5,DB=3x-19,AE=3$ and $EC=x-3,$ find x. [6 MARKS]

Answer 1

Each part : 3 Marks

(a) Using Basic Proportionality Theorem,
$\begin{array}{cc}& \frac{PL}{LQ}=\frac{PM}{MR}\\ \Rightarrow & \frac{PL}{14.4}=\frac{36}{10.8}\\ \Rightarrow & PL=\frac{36}{108}times14.4\\ \Rightarrow & PL=4.8cm\end{array}$


(b) Using Basic Proportionality Theorem,
$\begin{array}{cc}& \frac{AD}{DB}=\frac{AE}{EC}\\ \Rightarrow & \frac{x-5}{3x-19}=\frac{3}{x-3}\\ \Rightarrow & (x-5)(x-3)=3(3x-19)\\ \Rightarrow & x^2-3x-5x+15=9x-57\\ \Rightarrow & x^2-17x+72=0\\ \Rightarrow & x^2-9x-8x+72=0\\ \Rightarrow & x(x-9)-8(x-9)=0\\ \Rightarrow & (x-9)(x-8)=0\\ \Rightarrow & x-9=0orx-8=0\\ \Rightarrow & x=9orx=8\end{array}$