In a triangle ABC, points P and Q are on AB and AC, respectively, such that AP = 4 cm, PB = 6 cm, AQ = 5 cm and QC = 7.5 cm. If PQ = 6 cm, then find BC (in cm).
Answer & explanation
Correct answer: option 3
In \(\Delta \)ABC and \(\Delta \)APQ,
\(\frac{AP}{AB}\) = \(\frac{4}{10}\) or \(\frac{2}{5}\)
\(\frac{AQ}{AC}\) = \(\frac{5}{12.5}\) or \(\frac{2}{5}\)
So, \(\frac{AB}{AP}\) = \(\frac{AC}{AQ}\)
So, \(\Delta \)ABC is similar to \(\Delta \)APQ,
So, \(\frac{AB}{AP}\) = \(\frac{AC}{AQ}\)
So, \(\frac{PQ}{BC}\) = \(\frac{2}{5}\)
⇒ \(\frac{6}{BC}\) = \(\frac{2}{5}\)
⇒ BC = 6 x \(\frac{5}{2}\)
⇒ BC = 15
Therefore, BC is 15 cm.