Question

What is the length of of each side of an equilateral Triangle having an area of 4√3cm2

Answer 1

Given:

• Area of a equilateral triangle is 4√3cm².

To Find:

• Length of each side of the equilateral triangle.

Answer:

Now let us suppose each side of the equilateral triangle be x cm .

Now , here's a formula to find the area of the equilateral triangle.

$\large{\underline{\boxed{\red{\sf{\leadsto Area_{equi.\:\triangle}=\dfrac{\sqrt{3}}{4}a^2}}}}}$

where a is measure of each side length.

Using above formula,

$\sf{\implies 4\sqrt{3}cm^2= \dfrac{\sqrt{3}}{4}x^2}$

$\sf{\implies x^{2}=\dfrac{4\sqrt{3}\times4cm^{2}}{\sqrt{3}}}$

$\sf{\implies x^2 = 16cm^2}$

$\sf{\implies x=\sqrt{16cm^2}}$

$\sf{\implies x=\pm4cm}$

Since side can't be negative;

${\underline{\boxed{\red{\sf{\leadsto x=4cm}}}}}$

Hence length of each side of the equilateral triangle is 4cm