Question

An equilateral triangle and a regular hexagon have equal perimeters. What is the area of the triangle, if the area of the hexagon is 120?
I don't get it

Answer 1

the triangle can be formed by joining alternate vertices of the hexagon. So, if the hexagon has side s, the triangle has side s√3

Now the hexagon consists of sic equilateral triangles of side s, so its area is

6(s^2 √3/4) = 3√3/2 s^2

The triangle has area

√3/4 (s√3)^2 = 3√3/4 s^2

The ratio of areas is thus

(3√3/4 s^2) / (3√3/2 s^2) = 1/2

So the triangle has area 60