The perimeters of two 30-60-90 triangles are in the ratio 1:2. If the hypotenuse of the larger triangle is 12, find the sides of the smaller triangle.

Answer 1

Corresponding angles are same, so they're similar triangles. Ratio of the perimeters is exactly equal to ratio of the corresponding sides. Hypotenuse of larger triangle is 12, so for smaller one hypotenuse is 6.

Then relationship between the sides of that special right triangle (30-60-90) as like x, x√3 and 2x.

If the smaller side is x, the sides are x, x√3 and 2x

So 2x=6 (hypotenuse)

x=3

The length of sides of the smaller triangle are 3, 3√3 and 6.