If the areas of two isosceles triangles are in the ratio of $x^2: y^2$, then the ratio of their corresponding heights is:

x : y

Concept Used

Area of 1st triangle : Area of 2nd triangle = \( {Height\; of\; 1st\; triangle }^{2 } \) : \( {Height\; of\; 2nd\; triangle }^{2 } \)

Calculation

⇒  \( {x}^{2 } \) : \( {y }^{2 } \) = \( {Height\; of\; 1st\; triangle }^{2 } \) : \( {Height\; of\; 2nd\; triangle }^{2 } \)

⇒ x : y = Height of 1st triangle : Height of 2nd triangle

Therefore, the answer is x : y