Question

What is the perimeter of an equilateral triangle that has a height of 24m?

Answer 1

Answer:

The perimeter of an equilateral triangle that has a height of 24m is

Option C : 48 square root 3

Step-by-step explanation:

Given:

Height of the triangle =24 m

To Find:

The perimeter of an equilateral triangle  = ?

Solution:

Perimeter of the equilateral  triangle  =  3a

where a is the side of the triangle

Here the height is given as 24 m

Then from the figure

$Sin(60^{\circ}) = \frac{opposite}{hypotenuse}$

$Sin(60^{\circ}) = \frac{24}{x}$

$x = \frac{24}{Sin(30^{\circ})}$

$x= \frac{24}{\frac{\sqrt{3}}{2}}$

$x = \frac{24 \times2}{\sqrt{3}}$

$x = \frac{48}{\sqrt{3}}$

Now

The perimeter is

=> 3x

=>$3 \times \frac{48}{\sqrt{3}}$-------------------------(1)

Now we know that 3 = $\sqrt{3} \times \sqrt{3}$--------------------(2)

Substituting (2) in (1)

=>$(\sqrt{3} \times \sqrt{3}) \times \frac{48}{\sqrt{3}}$

=>$48\sqrt{3}$