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What is the area of an equilateral triangle with vertices a

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What is the area of an equilateral triangle with vertices a [#permalink] New post 20 Sep 2017, 01:48
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What is the area of an equilateral triangle with vertices at (–1, –3), (9, –3), and (m, n) where m and n are both positive numbers?

A. \(25 \sqrt{2}\)

B. \(50 \sqrt{2}\)

C. \(10 \sqrt{3}\)

D. \(25 \sqrt{3}\)

E. \(50 \sqrt{3}\)
[Reveal] Spoiler: OA

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Re: What is the area of an equilateral triangle with vertices a [#permalink] New post 22 Sep 2017, 05:21
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Once we are given two vertices of the triangle, since it is equilateral, we can find the length of the sides. Since the two given points are horizontally aligned their distance is the difference between their x coordinates, i.e. 10. Then, since half equilateral triangle is a 30-60-90 triangle, the height is 5sqrt(3). Then the area is easily computed as 10*5sqrt(3)/2 = 25*sqrt(3). Answer D!
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Re: What is the area of an equilateral triangle with vertices a [#permalink] New post 22 Sep 2017, 05:57
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Carcass wrote:
What is the area of an equilateral triangle with vertices at (–1, –3), (9, –3), and (m, n) where m and n are both positive numbers?

A. \(25 \sqrt{2}\)

B. \(50 \sqrt{2}\)

C. \(10 \sqrt{3}\)

D. \(25 \sqrt{3}\)

E. \(50 \sqrt{3}\)



Since it is already given that it is equilateral triangle

then all sides are equal and the distance between the sides of the co -ordinate points (–1, –3), (9, –3) is 10 (\(\sqrt{((-1-9)^2 +(-3 +3)^2}\))

Hence all sides are S = 10

since the area of equilateral triangle is \(\sqrt{3}\) /4 X side ^2

therefore putting the values we get \(\sqrt{3}\) /4 X 100 = 25\(\sqrt{3}\)
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Re: What is the area of an equilateral triangle with vertices a   [#permalink] 22 Sep 2017, 05:57
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