Question

if the area of equilateral triangle is 16root3 then find the height?.​

Answer 1

Given:

The area of the equilateral triangle is 16√3 unit sq.

To find:

The height of the equilateral triangle.

So,

We know that,

The formula for finding the area of an equilateral triangle is

$\boxed{\red{\sf{\frac{\sqrt{3}}{4}(side)^{2}\ unit^{2}}}}$

Now,

$\implies \frac{\sqrt{3}}{4}(side)^{2}=16 \sqrt{3}$

$\implies (side)^{2}=16 \sqrt{3} \div \frac{\sqrt{3}}{4}$

$\implies (side)^{2}=16 {\sqrt\not{3}} \times \frac{4}{\sqrt{\not3}}}$

$\implies (side)^{2}=16 \times 4$

$\implies (side)^{2} = 64$

$\implies side = \sqrt{64}$

$\implies \boxed{side = 8\ units}$

Thus, each side of the triangle is 8 units.

Now,

There is another formula to find the area of the triangle,

$\boxed{\bf{\frac{1}{2}\times base \times height}}$

So,

$\implies \frac{1}{2}\times base \times height = 16\sqrt{3}$

We got the side of the triangle, so base = 8 units

$\implies \frac{1}{2}\times 8 \times height = 16 \sqrt{3}$

$\implies 4 \times height = 16 \sqrt{3}$

$\implies height = \frac{16 \sqrt{3}}{4}$

$\implies height = 4 \sqrt{3}$

Hence,

The height of the equilateral triangle is 4√3 units.

Answer 2

Given :

Area = 16√3

To find:

Height = ?

Method:

Step by step explanation is in attachment.

Answer is 4√3 units

Hope it helps you