If the perimeter of an equilateral triangle is 18, the length of the altitude of this triangle is? (A. 6 square root of 3). (B. 6). (C. 3.) (D 3 square root of 3)

1 Answer
Dean R.
Apr 23, 2018

#3\sqrt{3}#

Explanation:

Lots of ways to do this one. Let's remember the altitude #h# of an equilateral triangle divides the side #s# in half, so we have a right triangle with sides #h# and #s/2# and hypotenuse #s#:

#h^2 + (s/2)^2 = s^2#

#h^2 = 3 / 4 s^2#

#h = sqrt{3}/2 s#

Here we know the perimeter:

# 3s = 18#

#s = 6#

#h = sqrt{3}/2 \times 6 = 3 sqrt{3} #

Choice D.

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