Area of an equilateral triangle is 4√3 cm2. Then the length of diagonal of a square whose side is equal to the height of equilateral triangle is?

Question

Area of an equilateral triangle is 4√3 cm2. Then the length of diagonal of a square whose side is equal to the height of equilateral triangle is?

2√6
3√6
2√3
3√2

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : 2√6

Given:

Area(A) of the equilateral triangle = 4√3 cm²

Formula used:

Area of an equilateral triangle = (√3/4)a²; a = length of the side of the triangle

Height of equilateral triangle = √3a/2

Here, a = length of the side of the triangle

Area of a square = Side²

Diagonal of a square = √2 side

x = length of the side of the square

Calculation:

According to the question:

Let a be the side of the equilateral triangle

(√3/4)a² = 4√3

⇒ a = 4 cm

Height of triangle = √3a/2 = (√3/2) × 4 = 2√3 cm = Side of the square

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Also, Height of triangle = side of square

Diagonal of the square = √2 side = √2 × 2√3 = 2√6

∴ Diagonal of the square = 2√6 cm