# The sides of such triangles are 2/1, and the area of the larger one is 36. find the area of the smaller triangle.

May 28, 2021 | education

| The area of arbitrary, larger and smaller, triangles is calculated by the formulas:

Sb = ½ * A * B * sinα;

Sm = ½ * a * b * sinα,

where A and B are the sides of the larger triangle, a and b are the sides of the smaller triangle, α is the angle between the corresponding sides of the larger and smaller triangles, in similar triangles these angles are equal.

Using the property of similar triangles, we write:

A: a = 2: 1.

B: b = 2: 1.

Therefore, A = 2 * a, B = 2 * b.

Let’s find the area ratio:

Sb / Sm = (½ * A * B * sinα) / (½ * a * b * sinα) = (A * B) / (a * b) = (2 * a * 2 * b) / (a * b ) = 4.

Hence,

36 / Sм = 4.

Sм = 9.

The area of the smaller triangle is 9.

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