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
[tex]Sin(60^{\circ}) = \frac{opposite}{hypotenuse}[/tex]
[tex]Sin(60^{\circ}) = \frac{24}{x}[/tex]
[tex]x = \frac{24}{Sin(30^{\circ})}[/tex]
[tex]x= \frac{24}{\frac{\sqrt{3}}{2}}[/tex]
[tex]x = \frac{24 \times2}{\sqrt{3}}[/tex]
[tex]x = \frac{48}{\sqrt{3}}[/tex]
Now
The perimeter is
=> 3x
=>[tex]3 \times \frac{48}{\sqrt{3}}[/tex]-------------------------(1)
Now we know that 3 = [tex]\sqrt{3} \times \sqrt{3}[/tex]--------------------(2)
Substituting (2) in (1)
=>[tex](\sqrt{3} \times \sqrt{3}) \times \frac{48}{\sqrt{3}}[/tex]
=>[tex]48\sqrt{3}[/tex]
