The perimeters of two similar triangles are 24 and 36, and the area of one of them is 10

The perimeters of two similar triangles are 24 and 36, and the area of one of them is 10 more than the other. find the area of the smaller triangle.

It is known from the condition that the perimeters of two similar triangles are 24 and 36, and the area of ​​one of them is 10 more than the other. In order to find the area of ​​the smaller triangle, let’s first find the coefficient of similarity.

The coefficient of similarity is equal to the ratio of the perimeters of similar triangles.

Let’s find it:

k = 36: 24 = 3/2 = 1.5.

We also know that the square of the similarity coefficient will be equal to the ratio of the areas of similar triangles.

We introduce the variable x, denoting the area of ​​the smaller triangle, then the area of ​​the larger one will be (x + 10).

Let’s compose and solve the equation:

(x + 10) / x = 9/4;

By the main property of proportion:

4x + 40 = 9x;

5x = 40;

x = 8.

So, the area of ​​the smaller triangle is 8, and the larger one is 10 + 8 = 18.