If the area of one regular triangle is 2 times the area of another regular triangle, then the ratio of their sides is 4.

If the area of one regular triangle is 2 times the area of another regular triangle, then the ratio of their sides is 4. Is this statement true or not?

Let this statement be true.

Let us express the side of the smaller of the triangles, for which we use the variable a.

Then, according to the statement, the side of the larger triangle can be represented as 4a.

The area of the former can be calculated as a * a * sin 60 °: 2.

And the area of the second will then be determined by the expression 4a * 4a * sin 60 °: 2.

Let’s find out whether the area of the second area of the first is 2 times:

(4a * 4a * sin 60 °: 2): (a * a * sin 60 °: 2) = 16.

16> 2.

Answer: No, not true.