Question

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

A) 36
B) 48
C) 48 square root 3
D) 48 Square root 2?

Answer 1

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

Option C : 48 square root 3

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)) = (opposite)/(hypotenuse)`

`Sin(60^(\circ)) = (24)/(x)`

`x = (24)/(Sin(30^(\circ)))`

`x= (24)/((√(3))/(2))`

`x = (24 *2)/(√(3))`

`x = (48)/(√(3))`

Now

The perimeter is

=> 3x

=>
`3 * (48)/(√(3))`-------------------------(1)

Now we know that 3 =
`√(3) * √(3)`--------------------(2)

Substituting (2) in (1)

=>
`(√(3) * √(3)) * (48)/(√(3))`

=>
`48√(3)`