SOLUTION: Find the side length of a equilateral triangle with an area of 12 radical 3.

Question 429889: Find the side length of a equilateral triangle with an area of 12 radical 3.
Found 3 solutions by Gogonati, poliphob3.14, richard1234:
Answer by Gogonati(855)   (Show Source): You can put this solution on YOUR website!
Solution:Let x cm the side of equilateral triangle, then half of its perimeter will be: 3x/2 cm. If we apply Heron's Formula of triangle area, we have:
, where p is half of perimeter and a=b=c=x cm the
sides of triangle.Substitute the given of our problem:
, squaring both sides,

,
x^3=432(8) => x=cubic root((432)(8)) => x=12(cubic root(2))cm
Done.
Answer by poliphob3.14(115)   (Show Source): You can put this solution on YOUR website!
Solution:Apply Heron's Formula for equilateral triangle with side x xm have:
, substituting our data we have:
, squaring both sides we have:

, divide by 3
, => x=fourth root of 2304 =>. Approximately x=7 cm.
Answer: The side of equilateral triangle with area 20.78 cm^2 is 6.93 cm.
Done.
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
One of the other tutors mis-applied Heron's formula. Instead of , it is . Heron's formula works, but it is somewhat tedious. Also, we could use the standard but that is boring, and there are faster solutions.

We can let the side length of the triangle be x. We can write the area in terms of two of the side lengths and the angle in between, i.e.

. Since ,

, approximately 6.928.
RELATED QUESTIONS
how do you find the area of an equilateral triangle with side length 2 radical... (answered by edjones)
Find the area of an equilateral triangle with side 12. (answered by ewatrrr)
What is the side length of an equilateral triangle whose area is radical 3 cm... (answered by Alan3354)
What would be the area of an equilateral triangle with a side length of 4 in simplest... (answered by neatmath)
A rectangle is inscribed fully inside an equilateral triangle. The triangle has a side... (answered by josgarithmetic)
A square is inscribed fully inside an equilateral triangle. The triangle has a side... (answered by richwmiller)
If an equilateral triangle has an area of 4, what is the length of a side in radical... (answered by CharlesG2)
what is the length of an altitude of an equilateral triangle with side lenghts 8 radical... (answered by DrBeeee)
find the area of an equilateral triangle with side length of... (answered by Gogonati)