Question

The ratio of the corresponding sides of two similar triangles is 2:5. If the area of ​​the larger triangle is 25 square meters, find the area of ​​the smaller triangle.

Answer 1

Let's denote the area of the smaller triangle as A₁ and the area of the larger triangle as A₂.

Since the two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Thus, we have:

(A₁/A₂) = (2/5)^2

Cross-multiplying, we get:

5^2 * A₁ = 2^2 * A₂

25 * A₁ = 4 * 25

25 * A₁ = 100

Dividing both sides of the equation by 25, we find:

A₁ = 100 / 25

A₁ = 4 square meters

Therefore, the area of the smaller triangle is 4 square meters.

Explanation: