Given are triangles ABC and MNK. Similar parties are referred to as 8: 5. The area of the ABC triangle is 25 cm

Given are triangles ABC and MNK. Similar parties are referred to as 8: 5. The area of the ABC triangle is 25 cm larger than the area of the MNK triangle. Find: area ABC and area MNK.

An error was made in the problem statement. It is not stated that triangles are similar. Parties that refer as 8: 5 not similar, but similar.

1. Find the coefficient of similarity (k) of triangles ABC and MNK:

By the condition of the problem, similar sides are related as 8: 5. Suppose AB: MN = 8: 5.

k = 8/5.

2. In accordance with the properties of such triangles, the ratio of their areas (S) is equal to

k² = 64/25. That is, S triangle ABC: S triangle MNK = 64/25.

4. We take the area of ​​the triangle ABC as x (cm²). The area of ​​the triangle is MNK (x – 25) cm².

5. Let’s make the proportion:

x / (x – 25) = 64/25;

25x = 64x – 1600;

39x = 1600;

x = 41 and 1/39 cm² – the area of ​​the triangle ABC.

Triangle area MNK = 41 and 1/39 – 25 = 16 and 1/39 cm².

Answer: the area of ​​the triangle ABC is 41 and 1/39 cm², the area of ​​the triangle is MNK

is 16 and 1/39 cm².