Question

The area of an equilateral triangle is $\frac{\sqrt{5043}}{4}$ sq.cm. The side of the equilateral triangle is:

• A. √23 cm
• B. √29 cm
• C. √47 cm
• D. √41 cm

Answer 1

Answer:

D. √41 cm

For an equilateral triangle, the area is:

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

Given:

$\frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{5043}}{4}$

Multiply both sides by 4:
$\sqrt{3} a^2 = \sqrt{5043}$

Square both sides:
$3a^4 = 5043$

$a^4 = 1681$
$a^2 = 41$
$a = \sqrt{41}$

$Final Answer: (\sqrt{41}) cm$