the ratios of the ares of two similar triangles is 4 : 9. What is the ratio of their altitudes drawn from corresponding sides?
2:3, the square root of the area ratio.
EF= 10cm, DF= 16 cm, DH= 48 cm what is the length?
This phone does not cope the square root any other that i want to use
To find the ratio of the altitudes drawn from corresponding sides, we need to understand the relationship between the areas of similar triangles and their corresponding sides.
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.
In this case, the ratio of the areas of the two similar triangles is 4:9. Let's call the ratio of their side lengths 'k'. So we have:
[(Length of corresponding side of Triangle 1) / (Length of corresponding side of Triangle 2)]^2 = 4/9
Let 'h1' and 'h2' be the altitudes drawn from corresponding sides of Triangle 1 and Triangle 2, respectively.
Now, we know that the area of a triangle is given by the formula (1/2) * (base) * (height). Since the area of a triangle is directly proportional to its height, the ratio of the altitudes is equal to the square root of the ratio of the areas of the triangles.
Therefore, the ratio of the altitudes is:
(h1 / h2) = sqrt(4/9)
Simplifying this expression, we get:
(h1 / h2) = 2/3
So, the ratio of the altitudes drawn from corresponding sides in two similar triangles is 2:3.