The area of two similar triangles are 324 cm2 and 289 cm2, respectively. What is the ratio of their corresponding altitudes?
Answer & explanation
Correct answer: option 4
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 \(\frac{18}{17}\).