Question

The area of an equilateral triangle is (64 x √3) cm^2. Find the length of each side of the triangle?

Answer 1

Answer :

Side of equilateral triangle = 16 cm

Solution :

We know that,

area of equilateral ∆ = √3/4 × side²

=> 64√3 = √3/4 × side²

=> 64 × 4 = side²

=> 256 = side²

=> side = ±√256

=> side = ±16

Rejecting the negative value, we get,

Side of equilateral triangle = 16 cm

Answer 2

Solution

The sides of the triangle are of the length 16 cm each

Given

Area of the Equilateral Triangle is 64√3 cm²

To find the measure of all sides in the traingle

$\boxed{\boxed{\sf Area \ of \ Equilateral \ Traingle = \dfrac{\sqrt{3}}{4}a^2}}$

Let the side of the triangle be x

Now,

$\sf \: 64 \sqrt{3} = \dfrac{ \sqrt{3} }{4} {x}^{2} \\ \\ \longmapsto \: \sf \: {x}^{2} = 256 \\ \\ \longmapsto \: \sf \: x = \pm \: \sqrt{256} \\ \\ \longmapsto \: \underline{ \boxed{ \sf \: x = 16 \: cm}}$

Here,x ≠ - 16 cm as a length measurement can't be negative