The area of an equilateral triangle is half the area of a square. The ratio of the height of the said triangle and an edge of the square is:

Question

Question

This question was previously asked in

RRC Group D Previous Paper 27 (Held On: 23 Sept 2018 Shift 2)

Answer 1

Formula used:

Area of the equilateral triangle = √3a²/4

Height of the equilateral triangle = √3a/2

Where, a is the side of the equilateral triangle

Area of the square = Side²

Calculation:

Now, A/Q

Let the side of the square be x

2 × Area of the equilateral triangle = Area of the square

⇒ 2 × (√3a2/4) = x²

⇒ √3a2/2 = x²

⇒ x = (√3a2/2)^(1/2)

⇒ x = a/√2

Now,

Height of the triangle/Edge of the square = {√3a/2}/x

⇒ {√3a/2}/{a/√2}

⇒ {3^{(1/2 - 1/4)}}/(2^{1 - 1/2})

⇒

Note:- There is mistake in the options of the official paper, the correct option is not provided.

Updated the correct Solution and the option.

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