Question

The length of each side of an equilatarel triangle having an area of 16√3 cm² is.
A) 10 cm
B) 4 cm
C) 6 cm
D) 8 cm​

Answer 1

Solution

Given :-

• Area of equilateral triangle = 16√3 cm²

Find :-

• Side of equilateral triangle

Explanation

we know,

Each side of an equilateral triangle have equal side .

Using Formula

★ Area of equilateral triangle = √3/4(Side)²

Let,

• Side be of equilateral triangle = x

So,

==> Area of equilateral triangle = √3/4(Side)²

==> 16√3 = √3/4 × (Side)²

==> (Side)² = 16√3 × 4/√3

==> (Side)² = 16 × 4

==> (Side)² = 64

==> (Side) = √64

==> (Side) = √(8×8)

==> (Side) = 8

Hence

• Each side of equilateral triangle will be = 8 cm

_______________

Since

• Our answer will be option number (D).

_______________

Answer 2

${\mathbf {\blue{S}{\underline{\underline{olution:-}}}}}$

$\mathfrak{\underline{AnswEr:-}}$

• The length of the each side of an equilateral triangle = 8 cm

$\mathfrak{\underline{Given:-}}$

• The area of an equilateral triangle is 16√3 cm².

$\mathfrak{\underline{Need\:To\: Find:-}}$

• The length of the each side of an equilateral triangle is = ?

${\mathbf {\blue{E}{\underline{\underline{xplanation:-}}}}}$

Let the side of triangle be a.

$\:\:\:\:\dag\bf{\underline \red{Then:-}}$

The area is given by:

$\sf { \frac{ \sqrt{3} }{4} a {}^{2} = \sqrt[16]{3} }$

$\longrightarrow \sf { \sqrt{3}\: a{}^{2} = 4 \times 16 \sqrt{3} }$

$\longrightarrow \sf {\sqrt{3} \: a {}^{2} = 64 \sqrt{3}}$

$\longrightarrow \sf {a {}^{2} = \frac{4 \sqrt{3} }{ \sqrt{3} } }$

$\longrightarrow \sf {a {}^{2} = 64}$

$\longrightarrow\large\boxed{\sf{\purple{a = 8}}}$

$\:\:\:\:\dag\bf{\underline{\underline \blue{Hence:-}}}$

• The length of the each side of an equilateral triangle is 8 cm.

$\:\:\:\:\dag\bf{\underline \green{Thus:-}}$

• Option (D) 8 Cm is correct option.

$\rule{200}{2}$