Question

If the area of the equilateral triangle is 25√3 square cm, then find its perimeter​

Answer 1

Answer:

30 CM is the perimeter

Step-by-step explanation:

let side of equilateral triangle be a

area of equilateral triangle = (√3)/4 x a^2

25√3 cm^2 = (√3)/4 x a^2

25 cm^2 = 1/4 x a^2

25 cm^2 x 4 = a^2

100 cm^2 = a^2

√100 cm^2 = a

10 cm = a

perimeter of equilateral triangle = 3 x side

=3 x a = 3 x 10 cm

= 30 cm

Answer 2

In context to question asked,

We have to determine the perimeter of equilateral triangle.

As we know that,

Equilateral triangle are those triangle which have equal sides.

As we know that,

Area of equilateral triangle will be $\frac{{\sqrt{3}}}{4}\:sides^2$

So, putting the value of area given in the question in above formula,

So, we will get,

$25{\sqrt{3}} = \frac{{\sqrt{3}}}{4}\:sides^2\\=>Sides^2=25\times 4\\=>Side = {\sqrt{100}}\\=>Side = 10\:cm$

Hence, for determining the value of perimeter we will add the length of all sides of equilateral triangle.

So, we will get the perimeter of triangle as,

$Perimeter = 10\times 3 = 30\:cm$

Hence, perimeter of triangle will be 30 cm.