Similar Triangles: Calculate Second Triangle Perimeter Given Areas 361cm² and 81cm²

Because area scales with the square of linear dimensions! If one triangle has sides twice as long, its area is four times larger (2²=4), but its perimeter is only twice as large.

It doesn't matter! The formula $\frac{P_2}{P_1} = \sqrt{\frac{S_2}{S_1}}$ works both ways. Just be consistent - if S₂ is in the numerator, then P₂ should be too.

That's fine! But check if the numbers under the square root are perfect squares first. Here, $\sqrt{81} = 9$ and $\sqrt{361} = 19$, so we get the clean fraction $\frac{9}{19}$.

Yes! This square root relationship works for any similar shapes - triangles, rectangles, circles, etc. The key is that the figures must be similar (same shape, different size).

The smaller area (81) should go with the smaller perimeter (18), and the larger area (361) with the larger perimeter (38). Also verify: $\left(\frac{18}{38}\right)^2 = \frac{81}{361}$ ✓