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What is the area of an equilateral triangle with vertices a [#permalink]
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Question Stats: 85% (01:27) correct 14% (02:53) wrong based on 7 sessions

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

_________________ Director Joined: 03 Sep 2017
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Re: What is the area of an equilateral triangle with vertices a [#permalink]
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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! Director Joined: 20 Apr 2016
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Re: What is the area of an equilateral triangle with vertices a [#permalink]
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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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