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

Given:

The area of two similar triangles is 324 cm2 and 289 cm2, respectively.

Concept used:

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding heights.

\({Area ~\triangle(ABC)\over {Area ~\triangle(DEF)}} = {[corresponding ~height~\triangle(ABC)]^2\over{[corresponding ~height~\triangle(DEF)]^2}}\)

Calculation:

Let the corresponding height of △ ABC = H₁

and the corresponding height of △ DEF = H₂

⇒ \({Area ~\triangle(ABC)\over {Area ~\triangle(DEF)}} = {[corresponding ~height~\triangle(ABC)]^2\over{[corresponding ~height~\triangle(DEF)]^2}}\)

⇒ (H₁)²/(H₂)² = 324/289

⇒ H1/H2 = √324/√289

⇒ H1/H2 = 18/17

∴ The correct answer is 18/17.