Question : The area of two similar triangles is 324 cm2 and 289 cm2, respectively. What is the ratio of their corresponding altitudes?
Option 1: $\frac{17}{18}$
Option 2: $\frac{17}{19}$
Option 3: $\frac{19}{17}$
Option 4: $\frac{18}{17}$
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Correct Answer: $\frac{18}{17}$
Solution :
The ratio of their altitudes will be equal to the ratio of the square roots of their area.
$\frac{A{_1}}{A{_2}} = \frac{h{_1}^2}{h{_2}^2}$
⇒ $\frac{324}{289} = \frac{h{_1}^2}{h{_2}^2}$
⇒ $\frac{h{_1}}{h{_2}}=\sqrt\frac{324}{289}$
⇒ $\frac{h{_1}}{h{_2}} = \frac{18}{17}$
Hence, the correct answer is $\frac{18}{17}$.
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