Question No. 4 The area of an equilateral triangle is half the area of a rhombus which in turn is equal to one third the area of a regular hexagon. Find the ratio of the length of each side of the triangle to that of the hexagon.​

Respuesta :

The ratio of the length of each side of the triangle to that of the hexagon is

What is equilateral triangle?

The triangle which has all the three sides equal in dimension is called the equilateral triangle.

According to the question,

Area of triangle = Area of rhombus = Area of hexagon

1/2 base x height = 1/2 diagonal1 xdiagonal2 = (3√3 / 2) side²

The triangle has equal base and height = a.

The hexagon has each side measuring b.

1/2 a² = (3√3 / 2) b²

Ratio of sides of triangle and hexagon is

a²/b² = 3√3

a/b = √ 5.19615

a/b = 2.2795

Thus, the ratio of each side of the triangle to that of the hexagon is 2.2795.

Learn more about equilateral triangle.

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