Question
What is the ratio of the areas of two similar triangles with side lengths 4cm and 6cm?
Answers
GPT-4o mini
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.
Let's denote the side lengths of the two similar triangles as \( a = 4 \) cm and \( b = 6 \) cm.
First, we calculate the ratio of the side lengths:
\[
\text{Ratio of sides} = \frac{a}{b} = \frac{4}{6} = \frac{2}{3}
\]
Now, we find the ratio of the areas by squaring the ratio of the sides:
\[
\text{Ratio of areas} = \left(\frac{a}{b}\right)^2 = \left(\frac{2}{3}\right)^2 = \frac{4}{9}
\]
Thus, the ratio of the areas of the two similar triangles is \( \frac{4}{9} \).
Let's denote the side lengths of the two similar triangles as \( a = 4 \) cm and \( b = 6 \) cm.
First, we calculate the ratio of the side lengths:
\[
\text{Ratio of sides} = \frac{a}{b} = \frac{4}{6} = \frac{2}{3}
\]
Now, we find the ratio of the areas by squaring the ratio of the sides:
\[
\text{Ratio of areas} = \left(\frac{a}{b}\right)^2 = \left(\frac{2}{3}\right)^2 = \frac{4}{9}
\]
Thus, the ratio of the areas of the two similar triangles is \( \frac{4}{9} \).