The ratio of the areas of two similar trapezoids is 1:9. What is the ratio of the

lengths of their altitudes?

1:9

I found the answer on the internet but don't know how to work it out... yet! :D Answer is 1/3

To find the ratio of the lengths of the altitudes of two similar trapezoids, we can take the square root of the ratio of their areas.

Given that the ratio of the areas of the trapezoids is 1:9, let's call the ratio of the lengths of their altitudes x:y.

Therefore, we have:
(x/y)^2 = 1/9

To find the values of x and y, we take the square root of the two sides of the equation:

sqrt((x/y)^2) = sqrt(1/9)

x/y = 1/3

Therefore, the ratio of the lengths of the altitudes is 1:3.

To find the ratio of the lengths of the altitudes of the two similar trapezoids, let’s first understand the relationship between the areas and altitudes of similar shapes.

In similar shapes, whether they are triangles, rectangles, or trapezoids, the ratio of their areas is equal to the square of the ratio of their corresponding lengths. Similarly, the ratio of their altitudes is equal to the ratio of their corresponding lengths.

Now, we are given that the ratio of the areas of the two similar trapezoids is 1:9. Let the lengths of the altitudes be a and b for the two trapezoids.

Using the area ratio, we have:

(area of trapezoid 1) / (area of trapezoid 2) = (altitude of trapezoid 1)² / (altitude of trapezoid 2)²

1/9 = a² / b²

To find the ratio of the altitudes, we need to solve for a/b.

Cross-multiplying the equation, we have:

9a² = b²

Taking the square root of both sides, we get:

3a = b

Therefore, the ratio of the lengths of the altitudes is 3:1.