Two triangles are similar. The ratio of their corresponding sides
1:4.
1. Find the ratio of their perimeters
2. What is the ratio of their areas
each side of the big one is 4 times the one in the small triangle
4a+4b+4c = 4(a+b+c)
the altitude of the big one is 4 timess the altitude of the small one
(1/2)(4h)(4b) = (16) (1/2) a b
The ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
In this case
P1 : P2 = 1 : 4
The ratio of the area of two similar triangles is proportional to square of the ratio of their corresponding sides.
In this case
A1 : A2 = ( 1 : 4 )² = 1 / 16
1. The ratio of their perimeters is equal to the ratio of their corresponding sides. Since the ratio of the corresponding sides is given as 1:4, the ratio of their perimeters will also be 1:4.
2. The ratio of their areas will be equal to the square of the ratio of their corresponding sides. Since the ratio of the corresponding sides is given as 1:4, the ratio of their areas will be (1^2):(4^2), which simplifies to 1:16.
To find the ratio of the perimeters of two similar triangles, you can simply multiply the ratio of their corresponding sides by the factor of similarity. In this case, the ratio of the corresponding sides is 1:4.
1. Find the ratio of their perimeters:
Let's say the perimeter of the first triangle is P1 and the perimeter of the second triangle is P2. Since the sides of the second triangle are four times larger, the ratio of their perimeters can be calculated as:
P1 : P2 = 1 : 4
So, the ratio of their perimeters is 1:4.
To find the ratio of the areas of two similar triangles, you can square the ratio of their corresponding sides.
2. Find the ratio of their areas:
Let's say the area of the first triangle is A1 and the area of the second triangle is A2. Since the sides of the second triangle are four times larger, the ratio of their areas can be calculated as:
A1 : A2 = (1:4)^2 = 1^2 : 4^2 = 1 : 16
So, the ratio of their areas is 1:16.