The area of an equilateral triangle is

The area of an equilateral triangle is $\frac{\sqrt{5043}}{4}$ sq.cm. The side of the equilateral triangle is:
एक समबाहु त्रिभुज का क्षेत्रफल $\frac{\sqrt{5043}}{4} cm^2$ है। समबाहु त्रिभुज की भुजा की लंबाई कितनी हैं?

$\sqrt{29}$ cm $\sqrt{41}$ cm $\sqrt{23}$ cm $\sqrt{47}$ cm

Detailed Solution & Logic

Correct Answer:

$\sqrt{41}$ cm

Area of an equilateral triangle = $ \frac{\sqrt{3}}{4}a^2 $
Given area = $ \frac{\sqrt{5043}}{4} $
$ \frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{5043}}{4} $
$ \sqrt{3},a^2 = \sqrt{5043} $
$ a^2 = \sqrt{\frac{5043}{3}} $
$ = \sqrt{1681} $
$ a^2 = 41 $
$ a = \sqrt{41} $
${\sqrt{41}\text{ cm}} $

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