Question

If the perimeter of an equilateral triangle is 90m. Find its area

Answer 1

3a = 90

a = 30

Area = √3/4 * a²

=√3/4 * 900

=225√3 m²

Answer 2

$\huge\mathbb{SOLUTION:-}$

Given tha perimeter of equilateral triangle =90m

Now we have to find the Area

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

Now a is the. side of triangle

So find the side of ∆

Let the side be a

Perimeter=Sum of all sides

$\sf\:\implies a+a+a=90\\ \\ \sf:\implies 3a=90\\ \\ \sf:\implies a=\cancel{\dfrac{90}{3}}\\ \\ \sf:\implies a=30$

Now the Area

$\sf:\implies Area=\dfrac{\sqrt{3}}{4}\times 30\times 30\\ \\ \sf:\implies Area=\dfrac{\sqrt{3}}{\cancel4}\times \cancel{900}\\ \\ \sf:\implies Area=\sqrt{3}\times 225\\ \\ \sf:\implies Area=225\sqrt{3}m{}^{2}$