Vertical heights of two similar triangles are 6 cm and 9 cm respectively. If the perimeter of the first triangle is 36 cm, find the perimeter of the…

For two similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides, altitudes, or medians. Therefore, $\frac{\text{Perimeter}_1}{\text{Perimeter}_2} = \frac{\text{Altitude}_1}{\text{Altitude}_2}$. Substituting the values, $\frac{36}{\text{Perimeter}_2} = \frac{6}{9} = \frac{2}{3}$. Solving gives $\text{Perimeter}_2 = \frac{36 \times 3}{2} = 54$ cm.