The perimeter of two similar triangles is 18 and 36, and the sum of their areas is 30. Find the area of the larger triangle

The perimeters of the triangles specified by the condition are related as 36/18 = 2, which means the coefficient of similarity of these triangles is 2: k = 2.

According to one of the similarity properties of triangles, the ratio of their areas is equal to the square of the similarity coefficient.

Let the area of the smaller of the given triangles be x, then the area of the larger of them is k ^ 2 * x = 2 ^ 2 * x = 4x. By condition, the sum of the areas of these triangles is 30. Let’s make the equation:

x + 4x = 30;

5x = 30;

x = 30/5 = 6.

Find the required area of the larger triangle: S = 4 * x = 4 * 6 = 24.