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Joined: 10 Apr 2015
Posts: 6218
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If an equilateral triangle has an area equal to
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12 Jan 2019, 06:51
12 Jan 2019, 06:51
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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
A. \(\sqrt{a}\)
B. \(2\sqrt{a}\)
C. \(6\sqrt{a}\)
D. 2a
E. 6a
Re: If an equilateral triangle has an area equal to
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12 Jan 2019, 08:05
12 Jan 2019, 08:05
3
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
A. \(\sqrt{a}\)
B. \(2\sqrt{a}\)
C. \(6\sqrt{a}\)
D. 2a
E. 6a
Explanation::
Area of \(Equilateral \triangle\)= \(\frac{(\sqrt3)}{4}* (Side)^2\)
Given,
\(\frac{(\sqrt3)}{4}* (Side)^2\) = \(a\sqrt3\)
or \((Side)^2 = 4a\)
or Side = \(2\sqrt{a}\)
Perimeter of \(equilateral \triangle\) = \(3 * side = 3 * 2\sqrt a = 6 \sqrt a\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If an equilateral triangle has an area equal to
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13 Jan 2019, 06:26
13 Jan 2019, 06:26
1
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
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√3
So, we can write: (side²)[(√3)/4)] = a√3
Divide 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
