Question

the area of an equilateral triangle is 16 root 3 cm square then what will be the length of each side of that triangle

Answer 1

Hey mate..
========

Given ,

Area of an equilateral triangle =

$16 \sqrt{3 } \: cm {}^{2}$

Length of the the other sides = ?

Let , the length of the other two sides be $a$

We know,

Area of an equilateral triangle =

$\frac{ \sqrt{3} }{4} (a) {}^{2}$

Thus,

$\frac{ \sqrt{3} }{4} (a) {}^{2} = 16 \sqrt{3}$

$= > (a) {}^{2} = 16 \sqrt{3} \times \frac{4}{ \sqrt{3} }$

$= > (a) {}^{2} = 64$

Therefore ,

a = 8 cm

Thus , The length of each side of the given equilateral triangle is 8 cm.

Answer 2

Concept:

In geometry, an equilateral triangle is a triangle with three equal-length sides.

The lines of symmetry of an equilateral triangle are its median, angle bisector, and altitude, which are all the same for each side. An equilateral triangle has an area of $\frac{\sqrt{3} }{4}(a)^2$.

Given:

The area of the equilateral triangle is $16\sqrt{3}cm^2$.

Find:

The length of each side of the triangle.

Solution:

In an equilateral triangle, the length of all the sides of the triangle is equal.

The area of the equilateral triangle is $16\sqrt{3}cm^2$.

The area of an equilateral triangle with side a is expressed as:

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

$16\sqrt{3}=\frac{\sqrt{3} }{4}(a)^2$

a² = 64 cm²

a =√64

a = 8 cm

The length of each side of the triangle is 8 cm.

#SPJ2