The sides of a triangle are 2: 3: 4. The larger side of a similar triangle is 36 cm. Find the perimeter of the second triangle?

Let k be the coefficient of proportionality, then the sides of the triangle will be respectively equal to 2k; 3k; 4k, because by condition, they relate as 2: 3: 4. The sides of a similar triangle are in the same ratio by the property of similar triangles, but with a different coefficient of proportionality: 2x; 3x; 4x. The large side of such a triangle is 36 cm, which means 4x = 36, we find x = 36: 4 = 9 (cm). To find the perimeter of the second triangle, you need to find the sum of all its sides: 2x + 3x + 4x = 9x = 9 ∙ 9 = 81 (cm).
Answer: the perimeter of such a triangle is 81 cm.