The height of an equilateral triangle is 4 StartRoot 3 EndRoot. What is the perimeter of the equilateral triangle? 12 units 12 StartRoot 3 EndRoot units 24 units 24 StartRoot 3 …

Question

asked Feb 24, 2021 222k views

2 Answers

Rayfleck · Answer 1 · 2021-02-28T15:40:46+0000

Answer:

The perimeter of the triangle is 24 units.

Explanation:

Given,

Height
$h=4\sqrt3$

We need to find the perimeter of the equilateral triangle.

Solution,

Firstly we will find out the side length of the triangle.

Since we know that the height of the equilateral triangle is equal to
$\sqrt3$ divided by 2 and then multiplied with side of the triangle.

The equation for height of the triangle can be written as;

$h=(\sqrt3)/(2)* a$

where 'a' is the side of the triangle.

On substituting the value of 'h', we get;

$4\sqrt3=(\sqrt3)/(2)* a$

On multiplying both side by
$(2)/(\sqrt3)$ using multiplication property, we get;

$4\sqrt3*(2)/(\sqrt3)=(\sqrt3)/(2)* a*(2)/(\sqrt3)\\\\8=a$

So we get the value of 'a' which is 8.

Here also given that the triangle is equilateral that means the length of all the three sides are equal.

And we know that the perimeter of a triangle is equal to sum of all the three sides.

$\therefore Perimeter = 8+8+8=24\ units$

Hence The perimeter of the triangle is 24 units.