SOLUTION: Given that the area of an equilateral triangle is 192 cm2, find its perimeter. Note: Your answer must be a number. No arithmetic operations are allowed. Can you explain to me

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Question 897667: Given that the area of an equilateral triangle is 192 cm2, find its perimeter.
Note: Your answer must be a number. No arithmetic operations are allowed.
Can you explain to me how I do this exercise?
Thanks
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Draw equilateral triangle. Label left and right sides, x; draw altitude and label it, y. label half of a bottom side as x/2. The x and y are related by Pythagorean Theorem, as y%5E2%2B%28x%2F2%29%5E2=x%5E2 and area is xy%2F2=192.

Solve the system for x, and then find 3x. You should have a value. The question you have means to report this value of 3x and therefore this value will not have operation symbols. You still need to use some operation symbols in the problem solving steps.



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Not show the steps here, but I found x=4sqrt%282%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Given that the area of an equilateral triangle is 192 cm2, find its perimeter.
Note: Your answer must be a number. No arithmetic operations are allowed.
Can you explain to me how I do this exercise?
Thanks 


Let each side of triangle be S

Since a 30-60-90 right triangle exists, and the hypotenuse is: S, then the base is: S%2F2, and the altitude is: %28S%2Asqrt%283%29%29%2F2

Now, since the area is 192_cm%5E2, we can say that: %281%2F2%29%28S%2F2%29%28S%2Asqrt%283%29%2F2%29+=+192_____%28S%5E2sqrt%283%29%29%2F8+=+192

S%5E2sqrt%283%29+=+8%28192%29 ------- Cross-multiplying

S%5E2+=+8%28192%29%2Fsqrt%283%29

S%5E2+=+%288%28192%29sqrt%283%29%29%2F%28sqrt%283%29%2Asqrt%283%29%29 ----- Rationalizing denominator

S%5E2+=+%288%28192%29sqrt%283%29%29%2F3

S%5E2+=+%288%2864cross%28192%29%29sqrt%283%29%29%2Fcross%283%29

S%5E2+=+512sqrt%283%29

S+=+sqrt%28512sqrt%283%29%29



Perimeter: 3S, or 3sqrt%28512sqrt%283%29%29

You can do the check!! 



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