The area of two similar triangles are 324 cm² and 289 cm², respectively. What is the ratio of their corresponding altitudes?

$\frac{18}{17}$

Formula to be used

\(\frac{area \;of \;triangle \; ABC}{area \; of \; triangle \; DEF}\) = (\(\frac{corresponding \;height \; of \; triangle \; ABC }{corresponding \;height \; of \; triangle \; DEF}\))²  

Calculations

Let the corresponding height of  \(\Delta \)ABC = H1

and the corresponding height of  \(\Delta \)DEF = H2

Putting into the formula

\(\frac{324}{289}\) = (\(\frac{H1}{H2}\))²

⇒ (\(\frac{H1}{H2}\)) = \(\frac{18}{17}\)

Therefore, the correct answer is \(\frac{18}{17}\).