Question

the area of an equilateral triangle is 64 root 3 cm square then find its height

Answer 1

here is ur answer.......

Answer 2

Answer:

Using formula:

Area of an equilateral triangle(A) is given by:

$A= \frac{\sqrt{3} }{4}a^2$ where a is the side of an equilateral triangle.

Height of an equilateral triangle(h) is given by:

$h = \frac{\sqrt{3}}{2}a$            ....[1]

As per the statement:

Area of an equilateral triangle is $64\sqrt{3}$ cm square.

using  Area formula we have;

$64\sqrt{3} =\frac{\sqrt{3} }{4}a^2$

Divide both sides by $\frac{4}{\sqrt{3} }$ we have;

$256 = a^2$

⇒$a = \sqrt{256} = 16 cm$

Substitute the value of a = 16 cm in [1] we have;

$h = \frac{\sqrt{3}}{2}(16)$

Simplify:

$h=8\sqrt{3}$ cm

Therefore, the height of an equilateral triangle is, $8\sqrt{3}$ cm