Question

the height of an equilateral triangle is $4sqrt{3}$. what is the perimeter of the equilateral triangle?
12 units
24 units
$24sqrt{3}$ units
$12sqrt{3}$ units

Explanation:

Step1: Recall height - side relation

For an equilateral triangle with side length $a$, the height $h=\frac{\sqrt{3}}{2}a$. Given $h = 4\sqrt{3}$.

Step2: Solve for side length

Set $\frac{\sqrt{3}}{2}a=4\sqrt{3}$. Cross - multiply to get $\sqrt{3}a = 8\sqrt{3}$. Divide both sides by $\sqrt{3}$, then $a = 8$.

Step3: Calculate perimeter

The perimeter $P$ of an equilateral triangle is $P = 3a$. Substitute $a = 8$ into the formula, so $P=3\times8=24$.

Answer:

24 units