Perimeter Ratio C37F46

1. **State the problem:** We are given that the areas of two similar plane figures are in the ratio $$36:25$$. We need to find the ratio of their perimeters. 2. **Recall the property of similar figures:** For two similar figures, the ratio of their areas is the square of the ratio of their corresponding linear dimensions (such as perimeters). 3. **Set up the relationship:** Let the ratio of the perimeters be $$\frac{a}{b}$$. Then the ratio of the areas is $$\left(\frac{a}{b}\right)^2$$. 4. **Use the given ratio of areas:** $$\left(\frac{a}{b}\right)^2 = \frac{36}{25}$$ 5. **Take the square root of both sides:** $$\frac{a}{b} = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5}$$ 6. **Interpretation:** The ratio of the perimeters of the two similar figures is $$6:5$$. **Final answer:** The ratio of the perimeters is $$6:5$$.