Question

The length of each side of an equilateral triangle of area 4√3 cm2, is
A. 4cm
B. 4/√3cm
C. √3/4cm
D. 3 cm

Answer 1

Given : area of an equilateral triangle is 4√3 cm².

To find :  Length of each side of an equilateral triangle.

We will find the length of each side of an equilateral triangle by using the formula for area of an equilateral triangle :  

Area of an equilateral triangle ,A =  √3a²/4

A =  √3a²/4

4√3 = √3a²/4

4√3 × 4 = √3a²

16√3 = √3a²

a² = (16√3)/√3

a² = 16

a = √16

a = 4 cm

Hence, the length of each side of an equilateral triangle is 4 cm.

Option (A) 4 cm is correct.

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Answer 2

Area of an equilateral triangle = $\tt{\frac{\sqrt{3} a^{2}}{4}}$

Here, the area is given equal to 4√3 sq cm. Thus, if we let side of triangle be equal to a cm:

$\tt{\frac{\sqrt{3} a^{2}}{4} = 4\sqrt{3} }$

=> a^2 = 16

=> a = 4

Thus, the side of triangle is (A) 4 cm.