Question

Area of equiangular triangle is 173.2 find its perimeter

Answer 1

Correct Question :

Area of equilateral triangle is 173.2 m. Find its perimeter.

Given :

Area of equilateral triangle is 173.2

Find :

Perimeter of equilateral triangle.

Solution :

We know that ..

$\bold{\boxed{Area \: of \: equilateral \: triangle \: = \: \frac{ \sqrt{3} }{4} {a}^{2} }}$

Put the known values in above formula

$\Rightarrow\:\dfrac{\sqrt{3}}{4}{a}^{2}\:=\:173.2$

$\Rightarrow\:a^{2}\:=\:\dfrac{173.2}{\sqrt{3}}\:\times\:4$

Now,

$\sqrt{3}\:=\:1.732$

$\Rightarrow\:a^{2}\:=\:\dfrac{173.2}{1.732}\:\times\:4$

$\Rightarrow\:a^{2}\:=\:100\:\times\:4$

$\Rightarrow\:a^{2}\:=\:400$

$\rightarrow\:a\:=\: 20$

Now,

$\bold{\boxed{Perimeter\:of\:triangle\:=\:3a}}$

Here..

a = side of triangle

And from above calculations we have a = 20

So,

$\Rightarrow\:3\:\times\:20$

$\rightarrow\:60$

∴ 60 m is the perimeter of equilateral triangle.