ΔABC is similar of ΔDEF.  The area of ΔABC is 144 cm² and the area of ΔDEF is 81 cm².  If the altitude of ΔABC = 8 cm, then the corresponding altitude of ΔDEF is?

6

\(\frac{Side\;of\;ΔABC}{Side\;of\;ΔDEF}\) = \(\frac{Altitude\;of\;ΔABC}{Altitude\;of\;ΔDEF}\) = \(\frac{\sqrt {Area\;of\;ΔABC}}{\sqrt {Area\;of\;ΔDEF}}\)

\(\frac{Altitude\;of\;ΔABC}{Altitude\;of\;ΔDEF}\) = \(\frac{12}{9}\) = \(\frac{8}{x}\)

 ⇒ x = \(\frac{9 × 8}{12}\) = 6 cm