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Find the altitude of an equilateral triangle whose side is 20.

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Bunuel
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Find the altitude of an equilateral triangle whose side is 20. [#permalink] New post   03 Dec 2020, 12:00
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Find the altitude of an equilateral triangle whose side is 20.

(A) 10
(B) \(10 \sqrt{2}\)
(C) \(10 \sqrt{3}\)
(D) \(20 \sqrt{2}\)
(E) \(20 \sqrt{3}\)
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C
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CrackverbalGMAT
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Re: Find the altitude of an equilateral triangle whose side is 20. [#permalink] New post   03 Dec 2020, 19:56
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Bunuel wrote:
Find the altitude of an equilateral triangle whose side is 20.

(A) 10
(B) \(10 \sqrt{2}\)
(C) \(10 \sqrt{3}\)
(D) \(20 \sqrt{2}\)
(E) \(20 \sqrt{3}\)



The altitude of an equilateral triangle of side a = \(\frac{\sqrt{3}}{2} * a\)


h = \(\frac{\sqrt{3}}{2} * 20 = 10\sqrt{3}\)


Option C

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Re: Find the altitude of an equilateral triangle whose side is 20. [#permalink] New post   03 Dec 2020, 20:13
IMO C

altitude of an equilateral triangle = √3/2 * side
=> altitude = 10√3

Or
the altitude of an equilateral triangle creates two equal right angle triangles and divides the base into two portions of equal size
considering one of the right angle triangles,
- the side will form the hypotenuse => hypotenuse = 20
- the altitude will be the height of the triangle => altitude = x
- and the base will be half of the length of the original base of the equilateral triangle => base = 20/2 = 10

=> by Pythagoras theorem
altitude = √(\(20^2\)-\(10^2\)) = 10√3
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Re: Find the altitude of an equilateral triangle whose side is 20. [#permalink] New post   06 Dec 2020, 09:15
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Bunuel wrote:
Find the altitude of an equilateral triangle whose side is 20.

(A) 10
(B) \(10 \sqrt{2}\)
(C) \(10 \sqrt{3}\)
(D) \(20 \sqrt{2}\)
(E) \(20 \sqrt{3}\)

Solution:

If we drop the altitude from a vertex of the equilateral triangle to the base that is opposite the vertex, we split the base into two equal parts. Furthermore, we’ve split the equilateral triangle into two congruent 30-60-90 right triangles. Since the base is a side of the triangle, its length is 20 and thus half its length is 10. Since half its length is the shorter leg of one of the 30-60-90 right triangles and the altitude is the longer leg, the altitude is 10√3 (recall that the ratio of the shorter leg to the longer leg of a 30-60-90 right triangle is x : x√3).

Answer: C
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Re: Find the altitude of an equilateral triangle whose side is 20. [#permalink]
06 Dec 2020, 09:15
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