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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 areas?

(1 point)
Responses

425

4 25

25

2 5

45

4 5

1

1

1 answer

To find the ratio of the areas of two similar triangles, you can use the fact that the ratio of their areas is the square of the ratio of their corresponding side lengths.

In your case, the side lengths of the two equilateral triangles are:

  • Left triangle: 2 cm
  • Right triangle: 5 cm

First, calculate the ratio of the side lengths:

\[ \text{Ratio of side lengths} = \frac{2}{5} \]

Next, square this ratio to find the ratio of the areas:

\[ \text{Ratio of areas} = \left(\frac{2}{5}\right)^2 = \frac{4}{25} \]

Thus, the ratio of their areas is \(\frac{4}{25}\).

So the correct answer is 4 25.