Question

In fig. 38, the value of k is

(a) $\frac{77}{8}$ (b) $\frac{73}{8}$ (c) $\frac{71}{8}$ (d) $\frac{75}{8}$

Answer 1

In triangle ABC, we have
$$\begin{gathered} \mathrm{Area}\mathrm{of}∆ABC=\frac{1}{2}\times BC\times AD=\frac{1}{2}\times AB\times CE \\ \Rightarrow BC\times AD=AB\times CE \\ \Rightarrow 14\times 11=16\times k \\ \Rightarrow k=\frac{14\times 11}{16}=\frac{77}{8} \end{gathered}$$
Hence, the correct option is (a).