If the length of the sides of two similar triangles are in the ratio 3:4, what is the ratio of the lengths of a pair of corresponding altitudes?

What is the ratio of their perimeter?

a. h1/h2 = 3/4.

b. P1/P2 = 3/4.

post.

To find the ratio of the lengths of a pair of corresponding altitudes of two similar triangles, we can use the fact that the ratio of their side lengths is given as 3:4.

Let's assume that the lengths of the corresponding altitudes are h1 and h2 for the two triangles respectively.

The ratio of the lengths of the corresponding altitudes is given by the same ratio as the sides, which is 3:4. Therefore, we have:

h1/h2 = 3/4

To find the ratio of their perimeters, we need to consider that the perimeter of a triangle is the sum of the lengths of its three sides.

Let the lengths of the sides of the first triangle be 3x and 4x, and the lengths of the sides of the second triangle be 3y and 4y (using the given ratio of 3:4).

To find the ratio of their perimeters, we need to compare the sums of the lengths of the sides of the two triangles:

Perimeter of triangle 1 = 3x + 4x + 5x = 12x
Perimeter of triangle 2 = 3y + 4y + 5y = 12y

Therefore, the ratio of their perimeters is 12x : 12y, which simplifies to x : y.

In conclusion:
- The ratio of the lengths of a pair of corresponding altitudes is 3:4
- The ratio of the perimeters is the same as the ratio of the lengths of the sides, which is 3:4.