GreenlightTestPrep wrote:
If an equilateral triangle has an area equal to \(a\sqrt{3}\), what is its perimeter, in terms of a?
A. \(\sqrt{a}\)
B. \(2\sqrt{a}\)
C. \(6\sqrt{a}\)
D. 2a
E. 6a
Useful formula:
Area of an equilateral triangle = (side²)[(√3)/4)]We're told the area =
a√3So, we can write: (side²)[(√3)/4)] =
a√3Divide both sides by √3 to get: (side²)/4 = a
Multiply both sides by 4 to get: side² = 4a
Take square root of both sides to get: side = √(4a) = (√4)(√a) = 2√a
So, ONE side of the equilateral triangle has length 2√a
So, the PERIMETER = 2√a + 2√a + 2√a = 6√a
Answer: C
Cheers,
Brent