The ratio of the areas of two similar trapezoids is 1/9. What is th eratio of the lengths of their altitudes?

1/3

for similar figures, area goes as square of ratio of dimensions

To find the ratio of the lengths of the altitudes of two similar trapezoids, we can use the fact that the ratio of the areas is equal to the square of the ratio of their corresponding side lengths.

Let's denote the lengths of the altitudes of the two similar trapezoids as h₁ and h₂ respectively.

Given that the ratio of the areas is 1/9, we have:

Area₁ / Area₂ = (h₁ * (a+b)) / (h₂ * (c+d)) = (h₁ / h₂) * ((a+b) / (c+d)) = 1/9

Here, a and b represent the lengths of the parallel sides of the first trapezoid, while c and d represent the lengths of the parallel sides of the second trapezoid.

Now, we can solve for the ratio of the lengths of the altitudes (h₁ / h₂):

(h₁ / h₂) = 1/9 * ((c+d) / (a+b))

Therefore, the ratio of the lengths of the altitudes of the two similar trapezoids is 1/9 multiplied by ((c+d) / (a+b)).