Question

A wire when bent in the form of an equilateral triangle encloses an area of 36√3

Answer 1

Acc to the question, a wire when bent in the form of an equilateral triangle encloses an area of 36√3.

We know, area of an equilateral triangle = ($\sqrt{3}$$a^{2}$)/4

or, ($\sqrt{3}$$a^{2}$)/4 = 36√3

or, $a^{2}$ = 36 x 4 = 144.

or, a = $\sqrt{144}$ = 12m.

Therefore length of the wire = perimeter of the triangle = 3 x a = 3 x 12 = 36m.

Answer 2

given area of equilateral triangle = 36√3

and we know formula for area of triangle = √3a²/4
[where, a = side of the triangle]

so, √3a²/4 = 36√3

a²/4 = 36

a² = (36 * 4)

a² = (6 * 2)

a = 12cm

Let the length of wire = L
and length of the wire = perimeter of equilateral triangle (sum of all sides)

L = a + a + a

L = 3(a)

L = 3(12)

L = 36cm