What is the scale factor of the two similar triangles?

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Here's the question:A triangle has side lengths 7 cm, 10 cm and 15 cm. A similar triangle to it has 25 times the area of the first triangle. Find the length scale factor between the two triangles.

My answer to this question is $\frac{1}{5}$. I used Heron's formula to solve for the area of the triangle and multiplied it by 25 to get the area of the other triangle. The ratio of their areas is $\frac{1}{25}$. But since the length scale factor is just needed, I just took the square root of $\frac{1}{25}$. But is there any other way to solve this without using any formula for area of triangle?

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1 Answer

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The scale factor for areas of similar two-dimensional figures is always $k^2$, where $k$ is the length scale factor. There was no need to compute the actual area of the triangles.

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