(a)[2]
Show that the ratio $\dfrac{\text{area of triangle }ABC}{\text{area of triangle }ADE}$ equals $\dfrac{AB \times AC}{AD \times AE}$.
(b)[3]
The ratio $\dfrac{\text{area of triangle }ABC}{\text{area of triangle }ADE}$ is given as $\dfrac{1}{3}$. Using the result from part (a), form an equation in $x$ and show that it reduces to $2x^2 - 19x + 6 = 0$.
(c(i))[3]
Solve the equation $2x^2 - 19x + 6 = 0$, and state each solution correct to $2$ decimal places.
(c(ii))[1]
State, with a reason, which one of these solutions is not valid for triangle $ABC$.
(d)[3]
If $\theta = 25$, calculate $BC$.