The equilateral triangles shown below are similar.
Two equilateral triangles are shown. The triangle on the left has side length measuring 2 cm. The triangle on the right has side length measuring 5 cm.
What is the ratio of their perimeters?
A.
4
25
B.
2
5
C.
4
5
D.
1
The perimeter of an equilateral triangle is three times its side length. Therefore, the ratio of the perimeters is equal to the ratio of the side lengths, which is $5/2$. Simplifying this ratio gives $\boxed{\textbf{(C) }4/5}$.
To find the ratio of their perimeters, we need to find the perimeter of each triangle and then divide them.
The perimeter of an equilateral triangle is equal to the sum of the lengths of its three sides.
For the triangle on the left with a side length of 2 cm, its perimeter is 2 + 2 + 2 = 6 cm.
For the triangle on the right with a side length of 5 cm, its perimeter is 5 + 5 + 5 = 15 cm.
Now, we can calculate the ratio of their perimeters:
Ratio = Perimeter of left triangle / Perimeter of right triangle
= 6 cm / 15 cm
= 2/5
Therefore, the correct answer is B. 2/5.
To find the ratio of their perimeters, we need to determine the ratio of their corresponding side lengths.
The side length of the equilateral triangle on the left is 2 cm, and the side length of the equilateral triangle on the right is 5 cm.
To find the ratio, we divide the side length of the larger triangle (5 cm) by the side length of the smaller triangle (2 cm):
Ratio = 5 cm / 2 cm
Simplifying this ratio gives us:
Ratio = 2.5
Therefore, the ratio of their perimeters is 2.5.
However, none of the answer choices provided match this result. Please double-check the answer choices or provide additional information if available.